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This question is worth 10 points. Each part is worth 0.5 points Consider a monopoly firm that can produce and sell some good. * The inverse demand function for this goed is P(gq) = a 1q. * The cost function of the monopolist is ('(q) Hrf. * (v, (3, and are strictly positive parameters. Please select the one correct option in each of the following questions The demand function is linear and decreasing function of P non-linear and decreasing function of P non-linear and increasing function of P linear and increasing function of g non-linear and decreasing function of non-linear and decreasing function of linear and increasing function of linear and decreasing function of The Revenue function R(q) = P(q) - qis non-linear, increasing, and concave function of linear, decreasing and convex function of non-linear and concave function of non-linear and convex function of @ non-linear, decreasing and convex function of linear, increasing, and concave function of The cost function is non-linear, decreasing and convex function of linear, decreasing, and convex function of linear, increasing, and concave function of non-linear, increasing, and concave function of The Marginal Revenue function is linear and increasing function of non-linear and increasing function of non-linear and decreasing function of linear and decreasing function of The Marginal Cost function is linear and decreasing function of non-linear and decreasing function of non-linear and increasing function of linear and increasing function of The Profit function is linear and convex function of non-linear and convex function of linear and concave function of non-linear and concave function of The Marginal Profit function is linear and decreasing function of non-linear and decreasing function of non-linear and increasing function of linear and increasing function of 4 The cost minimising quantity is Oa. 0 O b. undefined O c. 28 O d. 2( B+0) O e. Q(8+20) 2(8+0) Of. 4(B+0) The revenue maximising quantity is O a. 4(B+0) O b. undefined O C. 2(B+0) O d. (8+20) 2(B+0) O e. 28 Of. 0The profit minimising quantity is TEEY] undefined Which one of the following holds at the profit maximising quantity? marginal revenue is greater than marginal cost marginal revenue is greater than marginal cost marginal revenue equals marginal cost revenue is greater than cost revenue equals cost revenue is less than cost Which one of the following does not hold at the profit maximising quantity? profit function is locally concave slope of marginal profit function is zero slope of revenue function equals the slope of cost function slope of marginal profit function is positive The profit maximising quantity is The price at which the monopoly sells the good when it produces the profit maximising quantity is O a. 2(8+0) Ob. 0 O c. (8+20) 2(8+0) O d. 25 O e. 1( 8+0 ) Of. undefined The maximum profit the firm can make is O a. 1(8+0) Ob. 0 O c. undefined O d. a(8+20) 2(8+0) O e. 2(8+0) Of. 25 The Profit maximising quantity is O a. increasing in o, decreasing in , and decreasing in @ O b. decreasing in or, B and 0 O c. increasing in o, decreasing in B, and increasing in 0 O d. increasing in o, increasing in S, and decreasing in 0 O e. increasing in o, B and 0 The price at which the firm sells the good when it produces the profit maximising quantity is a. increasing in a, increasing in 3, and decreasing in 0 b. increasing in or, B and 0 O c. increasing in a, decreasing in B, and increasing in 0 O d. increasing in o, B and 0 O e. increasing in o, decreasing in B, and increasing inThe maximum profit of the firm is O a. increasing in o, decreasing in B, and increasing in 0 O b. increasing in a, increasing in B, and decreasing in 0 O c. decreasing in or, B and 0 O d. increasing in a, decreasing in 3, and decreasing in 0 O e. increasing in a, B and 0 The profit maximising quantity can be interpreted as O a. a function of the parameters in the problem O b. a function of P and 9 O c. a function of q O d. a function of P O e. a function of q The maximum profit of the firm can be interpreted as O a. a function of P and 9 O b. a function of q O c. a function of the parameters in the problem O d. a function of PThis question is worth 15 points. Each part is worth 3 points. Consider the following function from B* to B flx,y) = Alz,y) = Blx,y) -_)"'\\:.J:_f)\":lf-l.r + 2y) This function takes a point in I;-'_': as the input and produces a real number as the output. Now, please type in your answer to each of the following questions. The questions are designed such that each answer will be some integer. Output produced by [ at the input point(1, 1)is Answer: Evaluate the Marginal Rate of Substitution MRS, at the input point (1, 1) Answer: Is f concave or convex at the input point (1, 1)? (Write 0 if concave, 1 if convex) The unique global maximiser of f can be expressed as (z*, y*) = (m".m"). What is the value of 2/? Is f concave or convex at the input point(z, y ) where both & and are strictly positive? (Write 0 if concave, 1 if convex) Answer: |