James has 16 hours of labour to allocate between producing goods X and Y which means...

James has 16 hours of labour to allocate between producing goods X and Y which means that LX + LY = 16. He also has 4 units of capital to allocate KX + KY = 4. Production functions are X = 2KX1/4LX1/4 and Y = KY1/4LY1/4. His tastes for the two activities are symmetric U = XY. a. Derive James’ Production Possibilities Frontier. Put Y on the vertical axis. Provide a labelled PPF graph showing the combination of Y and X that is consistent with his tastes. Making reference to your diagram, define “consistency” in this context. b. James should allocate _____________ units of labour and ____________ units of capital to the production of Good X.

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Rahul Sunny answered 2 years ago

James has 16 hours of labour to allocate between producing goods X and Y which means...

James has 16 hours of labour to allocate between producing goods X and Y which means that LX + LY = 16. He also has 4 units of capital to allocate KX + KY = 4. Production functions are X = 2KX1/4LX1/4 and Y = KY1/4LY1/4. His tastes for the two activities are symmetric U = XY. a. Derive James’ Production Possibilities Frontier. Put Y on the vertical axis. Provide a labelled PPF graph showing the combination of Y and...

7. a) A firm producing two goods (X and Y) has the following profit (?) function:...

7. a) A firm producing two goods (X and Y) has the following profit (?) function: Profit: ? =80X-2X2 - XY-3Y2 +100Y Maximum Capacity: X+Y=12 What are the values of X and why that maximizes profits subject to the firm’s maximum capacity? b) Consider the following utility function for a consumer, who consumes goods X and Y whose prices are $8 and $12respectively. Utility function: U=XY+3X+Y If the consumer’s money income (budget is $112), what are the utility maximizing values...

Suppose that a consumer has a choice between two goods, X and Y. If the price of...

Suppose that a consumer has a choice between two goods, X and Y. If the price of X is $2 per unit and the price of Y is $5 per unit, how much of X and Y will the utility maximizing consumer purchase, assuming an income of $19? Use the information on total utility given below. Use a methodology that could be used in answering a more complex problem and show how you used this methodology. Trial and error or summing the different combinations...

Suppose a consumer has 60 hours per week to allocate between work and play, and the...

Suppose a consumer has 60 hours per week to allocate between work and play, and the hourly wage rate is $30. She chooses to have 20 hours of leisure and 40 hours of working. The government imposes a $10 per hour income tax. With the tax, the consumer chooses to have 25 hours of leisure. On a graph with “leisure hours per week” on the horizontal axis and “consumption in dollars” on the vertical to illustrate your weekly budget constraint,...

Suppose P (x, y) means “ x and y are real numbers such that x +...

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Waymire Ltd. currently uses a traditional costing system based on direct labour hours to allocate overhead....

Waymire Ltd. currently uses a traditional costing system based on direct labour hours to allocate overhead. This year, the company has budgeted to produce 1668 units of one of its products. Each unit requires 5 hours of direct labour. For the coming year, the company is considering changing to an activity based costing system by allocating overhead based on 3 activities. The following are the activities, budgeted total cost and cost drivers per activity for the upcoming year: Activity Cost...

A nation’s residents can decide to allocate their scarce resources either to producing consumption goods or...

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A consumer purchases two goods, x and y and has utility function U(x; y) = ln(x)...

A consumer purchases two goods, x and y and has utility function U(x; y) = ln(x) + 3y. For this utility function MUx =1/x and MUy = 3. The price of x is px = 4 and the price of y is py = 2. The consumer has M units of income to spend on the two goods and wishes to maximize utility, given the budget. Draw the budget line for this consumer when M=50 and the budget line when...

A consumer has demand for two different goods, x and y, which he chooses to maximize...

A consumer has demand for two different goods, x and y, which he chooses to maximize the utility function: U(x,y)=√x+√y (x≥0, y≥0) subject to the budget constraint: px+qy=m (m,p,q>0) where p is the price of good x, q is the price of good y, and m is total income a) Show that the utility function is concave b) Write out the Lagrangian for the constrained maximization problem, assuming consumer spends his full income c) Find the utility maximizing demands for...

The utility that James receives by consuming good X and good Y is given by u(X,Y)...

The utility that James receives by consuming good X and good Y is given by u(X,Y) = XY. 5.1) Draw the indifference curve associated with a utility level of 12 and the indifference curve associated with the utility level of 36. 5.2) Suppose that X costs $1 per unit and Y $3 per unit. James has $12 to spend on X and Y. Graph the budget line that he faces. 5.3) Derive James' demand functions. What is the utility-maximizing choice...

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James has 16 hours of labour to allocate between producing goods X and Y which means...

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