Microeconomics Answers

Consider the utility function 𝑈(𝑥, 𝑦) = 𝑥𝑦 + 𝑥, with 𝑀𝑈𝑥 = 𝑦 + 1 and 𝑀𝑈𝑦 = 𝑥. (Verify these.) 

a. is the assumption of “more is better” (non-satiation) satisfied for both goods x and y? 

b. does the marginal utility of 𝑥 diminish, remain constant, or increase as the consumer buys more 𝑥? Explain. 

c. what is 𝑀𝑅𝑆𝑥,𝑦? 

d. is 𝑀𝑅𝑆𝑥,𝑦 diminishing, constant, or increasing as the consumer substitutes 𝑥 for 𝑦 along an indifference curve? 

e. on a graph with 𝑥 on the horizontal axis and 𝑦 on the vertical axis, draw a typical indifference curve (not necessarily exactly to scale, but should reflect whether 𝑀𝑅𝑆𝑥,𝑦 is diminishing or not). Label the curve as 𝑈1. 

f. on the same graph, draw a second indifference curve 𝑈2, where 𝑈2 > 𝑈1

The demand and cost function for a company is estimated to be as follows: 

P = 100-8Q; TC = 50+80Q-10Q 2 + 0.6Q 3.

A.   What Price should it charge if it wants to maximize its profit in the short run?

B.    What price should it charge if it wants to maximize its revenue in the short run?

The demand and cost function for a company is estimated to be as follows: P = 100-8Q; TC = 50+80Q-10Q 2 + 0.6Q 3. Suppose the company lacks confidence in the accuracy of cost estimates expressed in a cubic equation and simply wants to use a linear approximation. Suggest a linear representation of this cubic equation.

a) Bruce had a rare encounter with the Almighty. The Almighty offered him 3 wishes of his preference. Bruce very shrewdly chose these 3 things in that order — lots of wealth, a popular life and never have to work again. The Almighty happily granted his three wishes to Bruce. Few weeks down the line, with the spread of coronavirus, Bruce found him to be affected by it. He has gone extremely pale and week, has lost his smell, has lost his taste, can barely walk by himself. Not happy with what he has been going through, he started blaming the Almighty for all this. Do you think that Bruce was acting as a rational being? Why or why not, explain your answer.