Suppose a firm’s multiproduct cost function is C(Q1, Q2) = 65 - 0.5Q1Q2 + 0.3Q12 +...

Suppose a firm’s multiproduct cost function is C(Q₁, Q₂) = 65 - 0.5Q₁Q₂ + 0.3Q₁² + 0.4Q₂², and management wishes to produce 12 units of each product (Q₁ = Q₂ = 12 units).

Determine the marginal cost of each product at the planned levels of production. Clearly show your steps and calculations.

Determine whether the multiproduct cost function exhibits economies of scope or not at the planned levels of production. Clearly show your steps and calculations.

Determine whether the multiproduct cost function exhibits cost complementarity or not at the planned levels of production. Clearly show your steps and calculations.

Discuss the economic implications of the outcomes in (b) and (c) above.

Expert Solution

Rahul Sunny answered 6 months ago

Suppose the utility function for goods q1 and q2 is given by U(q1, q2) = q1q2...

Suppose the utility function for goods q1 and q2 is given by U(q1, q2) = q1q2 + q2 6 (a) Calculate the uncompensated (Marshallian) demand functions for q1 and q2 2 (b) Describe how the uncompensated demand curves for q1 and q2 are shifted by changes in income (Y) or the price of the other good. 3 (c) Calculate the expenditure function for q1 and q2 such that minimum expenditure = E(p1, p2, U) 4 (d) Use the expenditure function...

1. Suppose the utility function for goods q1 and q2 is given by U(q1, q2) =...

1. Suppose the utility function for goods q1 and q2 is given by U(q1, q2) = q1q2 + q2 (a) Calculate the uncompensated (Marshallian) demand functions for q1 and q2 (b) Describe how the uncompensated demand curves for q1 and q2 are shifted by changes in income (Y) or the price of the other good. (c) Calculate the expenditure function for q1 and q2 such that minimum expenditure = E(p1, p2, U) (d) Use the expenditure function calculated in part...

Suppose the utility function for goods q1 and q2 is given by U(q1,q2)=q1q2 +q2 (a) Calculate...

Suppose the utility function for goods q1 and q2 is given by U(q1,q2)=q1q2 +q2 (a) Calculate the uncompensated (Marshallian) demand functions for q1 and q2 (b) Describe how the uncompensated demand curves for q1 and q2 are shifted by changes in income (Y) or the price of the other good. (c) Calculate the expenditure function for q1 and q2 such that minimum expenditure = E(p1, p2, U) (d) Use the expenditure function calculated in part (c) to compute the compensated...

Suppose the utility function for goods q1 and q2 is given byU(q1,q2)=q1q2 +q2 (a) Calculate the...

Suppose the utility function for goods q1 and q2 is given byU(q1,q2)=q1q2 +q2 (a) Calculate the uncompensated (Marshallian) demand functions for q1 and q2 (b) Describe how the uncompensated demand curves for q1 and q2 are shifted by changes in income (Y) or the price of the other good. (c) Calculate the expenditure function for q1 and q2 such that minimum expenditure = E(p1, p2, U) (d) Use the expenditure function calculated in part (c) to compute the compensated demand...

1. Suppose the utility function for goods q1 and q2 is given by U(q1,q2) = q1q2...

1. Suppose the utility function for goods q1 and q2 is given by U(q1,q2) = q1q2 + q2 (a) Calculate the uncompensated (Marshallian) demand functions for q1 and q2 (b) Describe how the uncompensated demand curves for q1 and q2 are shifted by changes in income (Y) or the price of the other good. (c) Calculate the expenditure function for q1 and q2 such that minimum expenditure = E(p1,p2, U) (d) Use the expenditure function calculated in part (c) to...

) Suppose that the firm’s total cost function is of the form C(y) = 100 +...

) Suppose that the firm’s total cost function is of the form C(y) = 100 + 10y + y^2 . Where does the average cost function reach a minimum? Consider the following demand curves: i. D(P) = 130 − 4P ii. D(P) = 120 − 2P iii. D(P) = 120 − 4P For which of these examples is the firm a natural monopoly? [There may be multiple tests to answer this question. Clearly state which one you are using. That...

Carl enjoys Coffee (q1) and smoothie (q2) and the utility function is: U=q1^2 + q2^2 Suppose...

Carl enjoys Coffee (q1) and smoothie (q2) and the utility function is: U=q1^2 + q2^2 Suppose that Carl has $100 spend on coffee and smoothies and the price of a pitcher of smoothie is $10 and the price of a coffee jar is $4. e) Derive Carl’s optimal bundle. Draw the graph of the budget constraint and show the optimal bundle on the graph. Draw a free hand indifference curve. It is not necessary to use the given utility function...

Suppose that the inverse demand function is described by, P = 60-4(q1 +q2), where q1 is...

Suppose that the inverse demand function is described by, P = 60-4(q1 +q2), where q1 is the output of the incumbent firm and q2 is the output of the entrant. Let the labor cost per unit w = 6 and capital cost per unit be r = 6. In addition, each firm has a fixed setup cost of f. (a) Suppose that in stage one the incumbent invests in capacity K1. Find the incum- bentís and entrantís best response functions...

Given a utility function: U(q1, q2) = q1 + q 2^2 where q1 and q2 is...

Given a utility function: U(q1, q2) = q1 + q 2^2 where q1 and q2 is the consumption of good 1 and good 2 respectively. and the budget constraint: p1q1 + p2q2 = Y where p1 and p2 are prices of good 1 and good 2 respectively, Y is the consumer’s income a. Holding p2 and Y fixed, find the demand function for good 2. b. Holding p1 and p2 fixed, find the functional form of the Engel curve for...

12. Suppose a firm’s cost function is C(q) = 3q2 + 10. (Show work) a. Find...

12. Suppose a firm’s cost function is C(q) = 3q2 + 10. (Show work) a. Find variable cost, fixed cost, average cost, average variable cost, and average fixed cost.(Hint: Marginal cost is given by MC = 6q.) b. Find the output that minimizes average cost.

Question