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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)
You are the manager of a firm that receives revenues of $40,000 per year from product X and $90,000 per year from product Y. The own price elasticity of demand for product X is -1.5, and the cross-price elasticity of demand between product Y and X is -1.8. How much will your firm’s total revenues (revenues from both products) change if you increase the price of good X by 2 percent? b. An individual consumes three goods, Q1, Q2, and Q3. The proportions of total Income devoted to the consumption of Q1 and Q2 are 75 and 15%, respectively. The income elasticities for Q1 and Q2 are 𝜀1,𝑀 = 0.75 and 𝜀2,𝑀 = −1.5, respectively. How would you classify the three goods? (5mks) c. Suppose that a firm’s marginal cost of production is constant at shs.25. Suppose further that the price elasticity of demand ( 𝜀𝑃 ) for the firm’s product is -5.0. i) Using optimal price formula what price should the firm charge for its product. ii) Suppose that 𝜀𝑃 = −0.5.What price should the firm charge for its product? Comment on this price.
Suppose the demand function for a firm’s product is given by 𝐿𝑛 𝑄𝑥 𝑑 = 7 − 1.5𝐿𝑛𝑃𝑥 + 2𝐿𝑛𝑃𝑦 − 0.5𝐿𝑛𝑀 + 𝐿𝑛𝐴 Where Px = $15, Py = $6, M = $40,000, and A =$350. a. Determine the own price elasticity of demand, and state whether demand is elastic, inelastic, or unitary elastic. (3mks) b. Determine the cross-price elasticity of demand between good X and good Y, and state whether these two goods are substitutes or complements. (3mks) c. Determine the income elasticity of demand, and state whether good X is a normal or inferior good. (3mks) d. Determine the own advertising elasticity of demand. (3mks
The market research Department of Paradox Enterprises has determined that the demand for fingolds is 𝑄 = 1,000 − 5𝑃 + 0.05𝑀 − 50𝑃𝑧 where P is the price of glibdips, M is income, and 𝑃𝑧 is the price of ballzacks. Suppose that P = $5, M = $20,000, and 𝑃𝑧 = $15. a. Calculate the price elasticity of demand for fingolds (3mks) b. Is the firm maximizing its total revenue at P = $5. If not, what price should it charge? (3mks) c. At P = $5, compute the income elasticity of demand for fingolds(3mks) d. At P = $5, cross-price elasticity of demand for fingolds.
