(A) A consumer's utility function is given by U(x, y) = xy P = 2, and...

    

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(A) A consumer's utility function is given by U(x, y) = xy P = 2, and Income M = 100. y 1/21/2 where P = 1, x - What quantity of good x can be purchased if the consumer allocates their entire income to good x? Good y? Find the optimal consumption bundle (x, y) and corresponding optimal utility level U What is meant by the rationality condition in consumer utility-maximization? (B) Now suppose P = 2with P = 2, and Income M = 100. y What quantity of good x can be purchased if the consumer allocates their entire income to good? Good y? Find the new optimal consumption bundle (x,y") and corresponding optimal utility level U What additional income (i.e. compensating variation) is needed by the consumer to reach the previous utility level U given these new prices? For the results in part A and part B, illustrate the budget constraint, indifference curve, and optimal bundles on an appropriately-labeled diagram Question 2 A firm's production function is given by f(K, L) = K¹/32/3. Assume that the factors of production of the firm are fully employed. The cost of capital (rent) is 10 and cost of labor (wages) is 5. The firm has an available budget of 100. - What is the factor mix (i.e. optimal bundle) of capital and labor used by the firm to maximize profits? Calculate the slope of the isoquant at a point Sketch an appropriately-labeled diagram showing the firm's budget constraint, isoquant, and factor mix What is the significance of the marginal rate of technical substitution (MRTS)? Why is the MRTS negative? Is this firm exhibiting decreasing returns to scale, constant returns to scale, or increasing returns to scale? Question 3 Consider a perfectly competitive market with a demand function given by Q = 100 - 2P, where Q represents the total quantity and Pis the market price. The firm's marginal cost is MC = 10. Calculate the equilibrium price P and quantity Q in this competitive market What decision rule will the firm use to decide output? Can a firm in a competitive market charge more than the market price for a good? Explain intuitively what happens to the firm's profits if they were to do so. Provide an example of a perfectly competitive market and a good (A) A consumer's utility function is given by U(x, y) = xy P = 2, and Income M = 100. y 1/21/2 where P = 1, x - What quantity of good x can be purchased if the consumer allocates their entire income to good x? Good y? Find the optimal consumption bundle (x, y) and corresponding optimal utility level U What is meant by the rationality condition in consumer utility-maximization? (B) Now suppose P = 2with P = 2, and Income M = 100. y What quantity of good x can be purchased if the consumer allocates their entire income to good? Good y? Find the new optimal consumption bundle (x,y") and corresponding optimal utility level U What additional income (i.e. compensating variation) is needed by the consumer to reach the previous utility level U given these new prices? For the results in part A and part B, illustrate the budget constraint, indifference curve, and optimal bundles on an appropriately-labeled diagram Question 2 A firm's production function is given by f(K, L) = K¹/32/3. Assume that the factors of production of the firm are fully employed. The cost of capital (rent) is 10 and cost of labor (wages) is 5. The firm has an available budget of 100. - What is the factor mix (i.e. optimal bundle) of capital and labor used by the firm to maximize profits? Calculate the slope of the isoquant at a point Sketch an appropriately-labeled diagram showing the firm's budget constraint, isoquant, and factor mix What is the significance of the marginal rate of technical substitution (MRTS)? Why is the MRTS negative? Is this firm exhibiting decreasing returns to scale, constant returns to scale, or increasing returns to scale? Question 3 Consider a perfectly competitive market with a demand function given by Q = 100 - 2P, where Q represents the total quantity and Pis the market price. The firm's marginal cost is MC = 10. Calculate the equilibrium price P and quantity Q in this competitive market What decision rule will the firm use to decide output? Can a firm in a competitive market charge more than the market price for a good? Explain intuitively what happens to the firm's profits if they were to do so. Provide an example of a perfectly competitive market and a good