5.  An annuity pays $20,000 per quarter for 25 years and the payments are made at the end of each quarter. The first payment is made at the end of the first quarter. If the annual interest rate is 8 percent compounded quarterly for the first 10 years, and 12 percent compounded quarterly thereafter, what is the present value of the annuity (i.e, value of the annuity now)?

6. Your objective is to have $4,000,000 in an account that earns 8% annual return when you retire in 40 years.

a) If you make an equal deposit at the end of every year to the account for the next 40 years, what is the annual deposit? Assume that your first deposit occurs at the end of next year.

b) You retire after 40 years and have $4,000,000 in the account as planned. You expect to live for another 25 years after retirement. Assume that you leave the $4,000,000 in the account that continues to earn 8% annual return.  You plan to make an equal withdrawal from the account every year for the next 25 years. The first withdrawal is made at the end of the first year after your retirement and the account balance would be depleted after you make the 25th How much can you withdraw at the end of each year for the next 25 years?

7. You have found your dream home. The selling price is $300,000. You will put $60,000 as down payment and obtain a 30-year fixed-rate mortgage loan at 4.5 percent annual interest rate for the rest.

a) You are required to make an equal payment every month for 360 months to pay off the balance on the loan. Assume that the first payment begins in one month after you obtained the loan. What will each monthly payment be?

b) If you want to pay off the remaining principal on your mortgage loan after 10 years (i.e., 120 months), how much will you have to pay? Assume that you have never missed your payments during the first ten years after you obtained the loan. The bank that you obtained the loan from imposes no charges for early payoff of the loan.

Camping Company manufactures camping tents from a lightweight synthetic fabric. Each tent uses the following standard material and labor cost.

The following data was recorded for February, the first month of operations:

Fabric purchased............................9,000 yards......................$5.00 per yard

Fabric used in production................7,000 yards

Direct labor used.............................3,400 hours......................$10.75 per hour

Actual number of tents produced:   1,650 tents

Required: Make sure you do not forget to label the variances U or F. You need to show your work either by cell reference or showing your calculation to the side.

1. Calculate the direct materials price and quantity variance and designate U or F. Please note that the materials price variance is based on actual material purchased and the quantity variance is based on material used.

Materials price variance

Materials Quantity variance

2. Calculate the direct labor rate and efficiency variances and designate U or F.

Labor rate variance

Labor Efficiency variance

3. Explain one possible reason for each of the preceding variances listed below.

Materials price variance

Materials quantity variance

Labor rate variance

Labor efficiency variance

You work for a marketing firm that has just landed a contract with Run-of-the-Mills to help them promote three of their products: splishy splashies, flopsicles, and mookies. All of these products have been on the market for some time, but, to entice better sales, Run-of-the-Mills wants to try a new advertisement that will market two of the products that consumers will likely consume together. As a former economics student, you know that complements are typically consumed together while substitutes can take the place of other goods.

Run-of-the-Mills provides your marketing firm with the following data: When the price of splishy splashies decreases by 20%, the quantity of flopsicles sold decreases by 22% and the quantity of mookies sold increases by 7%. Your job is to use the cross-price elasticity between splishy splashies and the other goods to determine which goods your marketing firm should advertise together.

Complete the first column of the following table by computing the cross-price elasticity between splishy splashies and flopsicles, and then between splishy splashies and mookies. In the second column, determine if splishy splashies are a complement to or a substitute for each of the goods listed. Finally, complete the final column by indicating which good you should recommend marketing with splishy splashies.

8. Substitutes, complements, or unrelated?

You work for a marketing firm that has just landed a contract with Run-of-the-Mills to help them promote three of their products: penguin patties, flopsicles, and kipples. All of these products have been on the market for some time, but, to entice better sales, Run-of-the-Mills wants to try a new advertisement that will market two of the products that consumers will likely consume together. As a former economics student, you know that complements are typically consumed together while substitutes can take the place of other goods.

Run-of-the-Mills provides your marketing firm with the following data: When the price of penguin patties increases by 4%, the quantity of flopsicles sold decreases by 5% and the quantity of kipples sold increases by 3%. Your job is to use the cross-price elasticity between penguin patties and the other goods to determine which goods your marketing firm should advertise together.

Complete the first column of the following table by computing the cross-price elasticity between penguin patties and flopsicles, and then between penguin patties and kipples. In the second column, determine if penguin patties are a complement to or a substitute for each of the goods listed. Finally, complete the final column by indicating which good you should recommend marketing with penguin patties.

8. Substitutes, complements, or unrelated? You work for a marketing firm that has just landed a contract with Run-of-the-Mills to help them promote three of their products: penguin patties, flopsicles, and mookies. All of these products have been on the market for some time, but, to entice better sales, Run-of-the-Mills wants to try a new advertisement that will market two of the products that consumers will likely consume together. As a former economics student, you know that complements are typically consumed together while substitutes can take the place of other goods. Run-of-the-Mills provides your marketing firm with the following data: When the price of penguin patties decreases by 5%, the quantity of flopsicles sold increases by 4% and the quantity of mookies sold decreases by 6%. Your job is to use the cross-price elasticity between penguin patties and the other goods to determine which goods your marketing firm should advertise together. Complete the first column of the following table by computing the cross-price elasticity between penguin patties and flopsicles, and then between penguin patties and mookies. In the second column, determine if penguin patties are a complement to or a substitute for each of the goods listed. Finally, complete the final column by indicating which good you should recommend marketing with penguin patties. Relative to Penguin Patties Recommend Marketing with Penguin Patties Cross-Price Elasticity of Demand Complement or Substitute Flopsicles Mookies

3. Profit maximization using total cost and total revenue curves

Suppose Ana runs a small business that manufactures shirts. Assume that the market for shirts is a competitive market, and the market price is $20 per shirt.

The following graph shows Ana's total cost curve.

Use the blue points (circle symbol) to plot total revenue and the green points (triangle symbol) to plot profit for shirts quantities zero through seven (inclusive) that Ana produces.

Calculate Ana's marginal revenue and marginal cost for the first seven shirts she produces, and plot them on the following graph. Use the blue points (circle symbol) to plot marginal revenue and the orange points (square symbol) to plot marginal cost at each quantity.

Ana's profit is maximized when she producesshirts. When she does this, the marginal cost of the last shirt she produces is, which is (less or greater) than the price Ana receives for each shirt she sells. The marginal cost of producing an additional shirt (that is, one more shirt than would maximize her profit) is, which is (Greater or less) than the price Ana receives for each shirt she sells. Therefore, Ana's profit-maximizing quantity corresponds to the intersection of the   curves. Because Ana is a price taker, this last condition can also be written as   .

Suppose many firms are working on a vaccine for a particular virus (as is currently the case). Once a successful vaccine is discovered, assume it can be produced by firms at a flat marginal cost of MC = 1. Suppose the demand for vaccines is given by QD = 5 − P. (a) (5) Draw the MC and demand curves on a clearly marked diagram. (b) (5) If this were a competitive market, what would the equilibrium price and quantity be? (c) (5) As discussed in class, what is a major reason that the government would grant monopoly power to the first firm to discover 2 the vaccine? In other words, what’s the problem with leaving this as a competitive market? (d) (5) Now, suppose one firm has monopoly power in this market. Let us think about this firm’s profit-maximizing choice. The firm can choose any quantity, from 0 to 5. As shown in class, fill out a table that has columns for quantity (Q), the associated price (P), the total revenue (TR), and the marginal revenue (MR). (e) (5) What is the firm’s profit-maximizing price and quantity? (f) (5) On a clearly marked diagram, show the dead weight loss associated with the monopoly outcome. (g) (5) Suppose the government is concerned that consumers are being hurt by this inefficiency. Consider the following response from the monopolist: “If you allow us to price discriminate, the market will be more efficient.” Discuss why the government would not be satisfied by this response to its concerns

5. Substitutes, complements, or unrelated?

You work for a marketing firm that has just landed a contract with Run-of-the-Mills to help them promote three of their products: splishy splashies, frizzles, and mookies. All of these products have been on the market for some time, but, to entice better sales, Run-of-the-Mills wants to try a new advertisement that will market two of the products that consumers will likely consume together. As a former economics student, you know that complements are typically consumed together while substitutes can take the place of other goods.

Run-of-the-Mills provides your marketing firm with the following data: When the price of splishy splashies increases by 5%, the quantity of frizzles sold decreases by 4% and the quantity of mookies sold increases by 5%. Your job is to use the cross-price elasticity between splishy splashies and the other goods to determine which goods your marketing firm should advertise together.

Complete the first column of the following table by computing the cross-price elasticity between splishy splashies and frizzles, and then between splishy splashies and mookies. In the second column, determine if splishy splashies are a complement to or a substitute for each of the goods listed. Finally, complete the final column by indicating which good you should recommend marketing with splishy splashies.