Question

In: Economics

intermediate microeconomic theory courses, with topics production, cost, and supply The book used in this course...

intermediate microeconomic theory courses, with topics production, cost, and supply

The book used in this course is Intermediate Microeconomics and Its Application, by walter nicholson

The question is :

1. It is known that the total revenue function is ?(?) = 45,75? − ?²
short-run cost function ??? (?) = ?³ - 12? ² + 60? + 40

A. Determine the function: Average cost, marginal cost, Fixed cost, variable cost Average revenue, marginal revenue and determine the demand function and the supply function (q) and draw it in a graph by showing the price and quantity balance

B. Calculate how many q in order to obtain maximum profit, the total income at the maximum profit level, the total cost at the maximum profit level and the maximum profit.

Expert Solution

A.

Given the total cost function : STC(q)=q³-12q²+60q+40, we can find the following,

Average Cost = TC/q

AC=q²-12q+60+(40/q)

Marginal cost = dTC/dq

MC=3q²-24q+60

Fixed Cost = 40

Variable cost = q³-12q²+60q

Average Variable cost = q²-12q+60

Given the total revenue function - R(q)=45.75? − ?², we can find the following

Average Revenue = Total revenue/q

AR = 45.75-q

Marginal revenue = dTR/dq

MR = 45.75-2q

Demand function in the short run is given by the average revenue function. Therefore

demand function = P=45.75-q

and supply is given by the MC function that is above the Average variable cost function

i.e. Supply = P=3q²-24q+60

The profit maximizing firm would produce at the level where MC=MR, at this point the firm earns supernormal profits (Shown by point A on the graph). The efficient level of production would be the level where the MC=AR (shown in the graph as point B)

b)

Considering the profit maximizing level which is given by MC=MR

3q²-24q+60=45.75-2q

q= 6.615 and the corresponding MC=32.519

At this level the price paid by buyers is equal to the level where q=6.615 intersects the AR curve. Therefore P = 39.135

Therefore the profit is given by difference between the price paid by the buyers and the marginal cost incurred by the sellers at the given level of q.

Profit = 39.135(6.615)-32.519(6.615)

Profit = 43.7648

Total income at this level = 39.135(6.615) = 258.878

Total Cost = (6.615)³-12(6.615)²+60(6.615)+40

TC = 201.261

Rahul Sunny answered 2 years ago

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