# Question

In Figure, the total benefit and total cost curves are represented by the following mathematical functions:

TB = TB (A) = 8A – 0.004 A2

and

TC = TC (A) = A + 0.006 A2

a. Find the marginal benefit function. Verify that points c, b, and d in Figure lie on the marginal benefit curve.

b. Find the marginal cost function. Verify that points c’, b, and d’ in Figure lie on the marginal cost curve.

c. Derive the net benefit function. Verify the slopes of net benefit at points M, c”, and d” in Figure.

d. Find the optimal level of activity and the maximum value of net benefit. Does your answer match Figure?

TB = TB (A) = 8A – 0.004 A2

and

TC = TC (A) = A + 0.006 A2

a. Find the marginal benefit function. Verify that points c, b, and d in Figure lie on the marginal benefit curve.

b. Find the marginal cost function. Verify that points c’, b, and d’ in Figure lie on the marginal cost curve.

c. Derive the net benefit function. Verify the slopes of net benefit at points M, c”, and d” in Figure.

d. Find the optimal level of activity and the maximum value of net benefit. Does your answer match Figure?

## Answer to relevant Questions

A decision maker wishes to minimize the cost of producing a given level of total benefit, B = 288. The cost function is C = 6x + 3y and the total benefit function is B = xy. Set up the Lagrangian and then determine levels of ...Bridget has a limited income and consumes only wine and cheese; her current consumption choice is four bottles of wine and 10 pounds of cheese. The price of wine is $10 per bottle, and the price of cheese is $4 per pound. ...Assume a consumer with the utility function U = U (X, Y) = (X + 2)(Y + 1)and the budget constraint (M = 95, Px = 10, and Py = 5): 95 = 10X 15Ya. Set up the constrained maximization problem, and derive the first-order ...Suppose demand takes the form Q = 36 P–1. a. Show that the price elasticity of demand is constant and equal to 21. b. Write the total and marginal revenue functions.At a management luncheon, two managers were overheard arguing about the following statement: “A manager should never hire another worker if the new person causes diminishing returns.” Is this statement correct? If so, ...Post your question

0