Microeconomics Answers

In a pure exchange economy with two goods, G and H, the two traders have Cobb-Douglas utility functions. Amos' utility is U_a= (G_a )^∝ (H_∝)^(1-∝) and Elise’s is U_e= (G_e)^β (H_e)^(1-β). What are their marginal rates of substitution? Between them, Amos and Elise own 100 units of G and 50 units of H. Thus, If Amos has G_a and H_a, Elise has G_e =100-G_a and H_e =50-H_a. 

Solve for their contract curve. Show all your calculations clearly from your marginal utilities.

A large number of deaths have been recorded since the outbreak of the COVID-19 pandemic. This has reduced the number of households able to work and therefore reduces the supply of labour.

Explain, using a demand-supply diagram, the impact of a decrease in the supply of labour on the equilibrium wage rate and the equilibrium level of employment.

Calculate how much of each service is produced under the following circumstances, which we label A,B, and C -All two spend all their time planting flowers (A) -All two spend all their time hunting deer (B) -All two spend half of their time planning flowers and half of their time hunting deer (C). -Simba only plants flowers, while Nala hunts deer (D) (2) Graph the production possibilities frontier (PPF) for this economy. Using your answers to part (1), identify points A, B, C and D on your graph. Please clearly draw the graph.

True or false: Being a risk-averse individual, you prefer a guaranteed payment of 50$ to a gamble that pays you 100$ with 50% chance and 0$ with 50% chance (note that this question is not related to goods X and/or Y).

Do the production functions below exhibit diminishing returns to labor (to get full credit, you will need to show mathematically whether or not these functions exhibit diminishing returns to labor –for example, answering only “yes” will get you no credit)?

(a) Q = F(K,L) = √1000K^3.5L². Make sure to 1) show the mathematical steps (3 pts) and 2) explain your answer (2 pts).

Suppose that the XYZ Corp. (which is a profit-maximizing enterprise) produces “gadgets” according to the following production function: Q = 300K + 100KL + 2000L - L^2 , where Q is the number of gadgets per year, K is the amount of capital (machines) that are used, and L is the number of workers employed per year. Gadgets sell for $100 each.

a) If XYZ has 10 machines, and workers cost $100,000/year (including benefits and direct ancillary expenses), how many workers should XYZ hire?

b) If the workers cost $120,000, how many workers should XYZ hire?

c) If workers cost $100,000 but gadgets sell for $80 each, how many workers should XYZ hire?

d) If XYZ instead has 20 machines, how many workers should it hire when workers cost $100,000 and gadgets sell for $100?

Give an example of a price-setting firm and explain why you describe them in that way.