13. Consider a market for homogeneous hamburgers produced in a constant cost competitive industry. Suppose there are 600 Type 1 consumers that each have a utility function of ?1(?, ?) = ?^0.1?^0.9 and 400 Type 2 consumers that each have a utility function of ?2(?, ?) = ?^0.2?^0.8, where x is hamburgers and y is a composite commodity representing the rest of the consumer’s consumption (assume ?? = 1). The income for both types of consumers is $210. Each hamburger producer has the following long-run total cost function: ?(?) = ?^3 − 50?^2 + 632?.

a. What is the long-run competitive equilibrium for hamburgers? Specifically find:

i. What is the long-run competitive market equilibrium price?

ii. What is the quantity produced per firm?

iii. What is the demand function for each Type 1 consumer?

iv. What is the demand function for each Type 2 consumer?

v. How much does each Type 1 consumer purchase?

vi. How much does each Type 2 consumer purchase?

vii. What is the market demand function?

viii. What is the market quantity demanded?

ix. How many firms are there in the market?

b. Now, consider the same market during an economic recession where consumer incomes fall to $140. Now what is the long-run competitive equilibrium for hamburgers? Specifically find:

i. What is the long-run competitive market equilibrium price?

ii. What is the quantity produced per firm?

iii. What is the demand function for each Type 1 consumer?

iv. What is the demand function for each Type 2 consumer?

v. How much does each Type 1 consumer purchase?

vi. How much does each Type 2 consumer purchase?

vii. What is the market demand function?

viii. What is the market quantity demanded?

ix. How many firms are there in the market?

c. Above we considered the market just for hamburgers, but now let’s think in terms of general equilibrium. Use a graph of the Production Possibilities Frontier (PPF) and an Edgeworth box to explain the effects of the recession on hamburgers (x) and all other goods (y). How did it affect the amounts of x and y produced? How did it affect the usage rate of labor and capital in the economy? Finally, relate your answers to the recent Great Recession experienced from 2007-2009 (and the slow recovery period after).

Q1 A research laboratory identified a gene X of medicinal value in a plant species. You are given a small fragment of DNA containing gene X and the cloning vector pZoom. Maps of the 4 kb cloning vector pZoom and the 10 kb plant DNA fragment are shown in Figure 1 and 2, respectively. The PCR primer pairs (shown in Figure 1) F1/R1, F2/R2 and F3/R3 amplify fragments of 0.1, 0.6 and 0.8 kb, respectively. The antibiotic resistance gene A and gene B code for chloramphenicol and streptomycin resistance, respectively. The three restriction enzymes that cut this vector are BamHI, XbaI and HindIII represented on the map as enzymes I, II and III, respectively. You are given purified DNA of both the vector and the gene X containing DNA fragment at 0.2 µg/ul. Create a recombinant plasmid containing the complete gene X in the provided cloning vector pZoom. a. Design restriction digestion reactions using appropriate enzymes in such a way that you get a final concentration of 50 ng/µl for the digested vector and for the plant DNA (insert DNA) in the reaction. Your digestion should include all components in a 20 µL reaction. All enzymes are supplied with a concentration of 10 units/µL; you may use 1 µL of the enzyme in each reaction. Buffers for each enzyme are available as 10 times concentrated (10X) stocks. b. Generate three ligation reactions with 1:1, 2:1 and 3:1 molar ratios of the insert and the vector DNA. Your ligation should include all components in a 30 µL reaction. Keep the vector amount fixed at 100 ng per ligation reaction. You are provided with 10 x ligase buffer and DNA ligase (0.5 U/µL) to set up your ligations. c. Develop a strategy to select transformants and a quick method to screen recombinants; show your screening method using a figure. Predict the expected results with an explanation. d. Devise a restriction analysis method to confirm the desired recombinant; use a single most appropriate enzyme. Calculate the expected sizes of the restriction fragments from each, the vector and the desired recombinant. e. Devise a PCR strategy to confirm the desired recombinant. Calculate the expected sizes of the PCR fragments from the desired recombinant in a multiplex PCR including all three primer pairs. How will these sizes differ from the same multiplex PCR if the template is vector DNA instead of the recombinant plasmid?

A pharmacist wants to test whether a new kind of sleeping pill would be effective to increase the hours of sleep for people who take it. A random sample of 10 persons (Group A) was given the new pills and another random sample of 13 persons (Group B) was given the old pills.

Their sleep in hours were recorded as follows:

Mean of group A = 8.9 and Standard Deviation of group A = 0.8

Mean of Group B = 8.5 and standard Deviation of group B = 0.5

Construct a 95% confidence interval for the difference of the average hours of sleep that would be obtained for the people taking the new pills over the people taking the old pills. State the assumptions made.

You are an entrepreneur starting a biotechnology firm. If your research is​ successful, the technology can be sold for $21 million. If your research is​ unsuccessful, it will be worth nothing. To fund your​ research, you need to raise ​$4.8 million. Investors are willing to provide you with ​$4.8 million in initial capital in exchange for 30% of the unlevered equity in the firm.

a. What is the total market value of the firm without​ leverage?

b. Suppose you borrow ​$0.8 million. According to​ MM, what fraction of the​ firm's equity will you need to sell to raise the additional​$4.0 million you​ need?

c. What is the value of your share of the​ firm's equity in cases ​(a​) and ​(b​) above?

Determine the amounts of the solutes necessarry to prepare the indicated solutions.

A) 4L Dialysis Buffer (25mM HEPES, 0.01% (v/v) Triton X-100, 300mM NaCl, 2.5M Urea)

B) 250mL 25x MES running buffer (1x= 50mM MES, 50mM Tris, 0.1% (w/v) SDS, 1mM EDTA)

C) 1:15,000 SYBR Green (25mg/mL0 in 80mL 0.8% agarose

D) What is the final micromolar concentration of SYBR Green in the agarose solution in Part C?

Formula Masses

Tris: 121.14

NaCl: 58.44

HEPES: 238.3

Urea: 60.06

MES: 195.24

EDTA:292.24

SYBR Green: 509.73

In a hypothetical experiment, electrical current of 15 AMPs driven by an applied potential of 100 volts passes through a cylindrical rod (3 mm in diameter and 7 cm long). Recall, the power is calculated by power(Watts) = potential(VOLTS) x current(AMPS). The electrical power heats the cylindrical rod to a high temperature. The rod is inside of a ceramic tube (ID = 12 mm). The wall temperature of the ceramic tube is 600 C (maintained at this stead temperature by air cooling on the outside). Assuming that convection and conduction between the resistor and the ceramic tube are negligible compared to thermal radiation, estimate the surface temperature of the rod. The emissivity of the ceramic tube is 0.9 and the emissivity of the resistor is 0.8.

1. Write the chemical equation for the reaction of an antacid containing magnesium hydroxide, Mg(OH)₂, with stomach acid (hydrochloric acid, HCl) and then balance the equation.

2. If a tablet of the antacid neutralized 41.4 mL of 0.150 M hydrochloric acid then how many grams of magnesium hydroxide was in the tablet?

(Show calculation)

3.Concentrated gastric acid is about 0.16 molar in concentration (0.16 M HCl), corresponding to a pH of 0.8. In the stomach, however, the solution becomes diluted to a pH between 1 and 2. Using the information from Q.5 calculate how many milliliters of gastric acid can be neutralized by 1 tablet of antacid?

(Show calculation)

A state policymaker is thinking about reducing taxes to boost the local GDP. However, she is concerned about negative effects on the budget and orders a survey to gauge her voter’s consumption behaviour. The relevant information is summarized below.  

C = 600 + 0.8(DI)

Multiplier:

1 / 1−mpc

14. What is the size of the multiplier?

15. Assume she goes through with her plan and reduces taxes. As a consequence, she generates a tax revenue of T=100. By how much will consumption increase? By how much Savings?

16. Use your results from Q14 and Q15 to calculate the eventual increase in GDP resulting from the tax policy.

Answer two (2) of the following essay questions.

1) How do automatic stabilizers, on both the expenditure and revenue sides of the budget, respond when the economy is in 1) a contractionary 2) an expansionary gap?

2) How much should the government 1) increase spending or 2) cut taxes when the economy is in a contractionary gap equal to 500 billion and the MPC equals 0.8.

3) According to the classical school of economists, the economy is self-correcting. Explain why the economy will automatically move to long run equilibrium (potential output) when it is in an expansionary and in a contractionary gap.

4) Give an account of how an increase in government spending can lead to an increase in the trade deficit.