Given the long run cost equation of a firm as tcq 35q 5q2 q3...

Given the long-run cost equation of a firm as TC(Q) = 35Q - 5Q^2 + Q^3, find the: a) AC and MC equation (2 points) b) Output range the production function exhibits economies of scale and diseconomies of scale. (4 points) c) Estimate the output elasticity of output in the economies and diseconomies region

Transcript

00:01 We're given a cost schedule of a firm and we're told that the total fixed cost is 100.

00:08 We're to calculate the average variable and marginal cost at each given output level.

00:14 And we're given the total cost at outputs 1, 2, 3 and 4.

00:19 And the firm in sub -question a operates in the perfect competition market where the demand and supply equations are given by p is equal to 270 minus q, p is equal to 150 plus q.

00:37 Respectively we're to find the profit or loss done by the firm under the condition of profit maximization.

00:45 And we're to present the answer with a graph.

00:50 So given fixed cost as 100, the total cost minus fixed cost and the average variable cost is total variable cost over quantity.

01:06 The marginal cost is the change in total cost over change in quantity.

01:11 So given the demand and supply equations at equilibrium, demand is equal to supply.

01:17 So 270 minus q is equal to 150 plus q and q is equal to 60.

01:24 We put this in the value of q in supply function.

01:27 P is equal to 150 plus 60 which is equal to 210.

01:33 So under the perfect competition market, a firm is producing where p is equal to mc.

01:39 So the profit is the total revenue minus total cost and total revenue is equal to p times q which is 210 times 60 and this is 12 ,600.

01:54 The total cost is 150q plus q raised to power 2 divided by 2 plus c where c is the fixed cost...

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