Microeconomics Answers

Please assist, Thank you

A firm has the following revenue and cost functions:

           TR      =         120Q – 2Q²

           TC      =         200 +60 Q + Q²

Determine the level of output at which the firm maximizes its total profit

Question 3: Suppose the inverse demand function for good X is given as P=100-2Q. Find

the price elasticity of demand when Q=40 units. What can you say about the type of the good

looking at the price elasticity of demand that you calculate in the first part?

The satisfaction gained by consuming x units of good 1 and y units of good 2 is measured by the utility function

U = 2x2 + 5y3

Currently an individual consumes 20 units of good 1 and 8 units of good 2.

(a) Find the marginal utility of good 1 and hence estimate the increase in satisfaction gained from consuming one more unit of good 1.

(b) Find the marginal utility of good 2 and hence estimate the increase in satisfaction gained from consuming one more unit of good 2

Suppose that the marginal rate of substitution is 2, the price of X is sh 3,and the price of Y is sh.1 a. If the consumer obtains 1 more unit of X, how many units of Y must be given up in order to keep utility constant? b. If the consumer obtains 1 more unit of Y, how units many of X must be given up in order to keep utility constant? c. What is the rate at which the consumer is willing to substitute X for Y? d. What is the rate at which the consumer is able to substitute X for Y ?

Suppose that a consumer consumes two goods X and Y and derives utility according the following utility function where U = 25X2/5Y 3/5 where α = 2/5 and β = 3/5 a. If Px is the price of good X and Py is the price of good Y and the consumer’s income is M. Derive the demand functions for the two goods X and Y b. If Px is shs 15 and Py is shs 10 and the consumer has shs.800 to spend on the two goods what are the optimal quantities of X and Y that maximize the consumer’s utility? c. Using the information in b above show that the values of α and β represent the proportion of the consumer’s income spent on good X and good Y respectively

A consumer must divide shs.250 between the consumption of product X and product Y. The relevant market prices are Px = shs 5 and Py = shs.10. a. Write the equation for the consumer’s budget line. b. Illustrate the consumer’s opportunity set in a carefully labelled diagram. c. Show how the consumer’s opportunity set changes when the price of good X increases to shs.10. How does this change the market rate of substitution between goods X and Y?

One most commonly used utility function is the Cobb-Douglas utility function which of the form 𝑼(𝑿, 𝒀) = 𝑿 𝜶𝒀 𝜷 where α and β are positive constants. a. Show that this function exhibits diminishing marginal utility for both goods X and Y (4mks) b. Show that the indifference curves of this utility function are convex (i.e show that is there is diminishing marginal rate of substitution between X and Y) 

Explain, in plain words, what the R-square in this regression indicates. The demand function for good X is 𝐿𝑛𝑄𝑥 𝑑 = 𝑎 − 𝑏𝐿𝑛𝑃𝑥 + 𝑐𝐿𝑛𝑀 + 𝑒 . Where 𝑃𝑥 is the price of good X and M is income. Least squares regression reveals that â = 7.42 , bˆ = 2.81, cˆ =0.34, a. If M = 55,000 and 𝑃𝑥= 4.39, compute the own price elasticity of demand based on these estimates. Determine whether demand is elastic or inelastic. (4mks) b. If M = 55,000 and 𝑃𝑥= 4.39 , compute the income elasticity of demand based on these estimates. Determine whether X is a normal or inferior good

The demand function for good X is 𝑄𝑥 𝑑 = 𝑎 − 𝑏𝑃𝑥 + 𝑐𝑀 + 𝑒 . Where 𝑃𝑥 is the price of good X and M is income . Least squares regression reveals that â = 8.27, bˆ = 2.14, cˆ = 0.36, 𝜎â = 5.32, 𝜎𝑏ˆ = 0.41, and 𝜎𝑐ˆ = 0.22. The R-squared is 0.35. a. Compute the t-statistic for each of the estimated coefficients. (4mks) b. Determine which (if any) of the estimated coefficients are statistically different from zero. (4mks) c. Explain, in plain words, what the R-square in this regression indicates. (

Cost of producing Product X Cost of producing

Country A $10 $8

Country B $20 $5

(i) Without a trade what is the cost of producing product X for

country A and which one for B? (15 Marks)

(ii) Which country has a comparative advantage for product X and

product Z and why? (15 Marks)

(iii) Which country has an absolute advantage for both products and

why? (15 Marks)

(iv) If the two countries trade with each other which product will

prefer to export and why? (15 Marks)