Question

Suppose you are given the following demand and total cost functions for a firm that produces video games: Qd=60−P(1)

TC=1/2​Q² Let quantity be in millions of units. Use this information to answer the following:
(a) Set up the profit maximization problem.
(b) Find the equilibrium price and quantity.
(c) Identify the average revenue, marginal revenue, average total cost, and marginal cost functions.
(d) Plot the average revenue, marginal revenue, marginal cost, and average total cost curves Be sure to label the equilibrium price and quantity and the rectangle that shows the profit level.
(e) Find the price elasticity of demand at the equilibrium price and quantity.
(f) What is the price markup over marginal cost. What gives the firm the ability to set prices well above marginal cost?l]

Answer 1

(a) The profit maximization problem is to maximize π = TR - TC, where TR is total revenue and TC is total cost.

(b) Equilibrium price (P) is $30 million per unit and equilibrium quantity (Q) is 30 million units.

(c) Average revenue (AR) = P = 60 - Q/2, Marginal revenue (MR) = 60 - 2Q, Average total cost (ATC) = 1/2Q, Marginal cost (MC) = Q.

(d) The curves show AR, MR, MC, and ATC intersecting at the equilibrium point of P=$30 and Q=30M; the profit rectangle lies between ATC and AR/MR curves.

(e) Price elasticity of demand at equilibrium is -1, indicating unitary elasticity.

(f) Price markup over marginal cost is $30, resulting from market power and differentiated products.

Step-by-step explanation:

The profit maximization problem involves finding the level of output where a firm's revenue exceeds its costs. In this scenario, the equilibrium price and quantity are reached where demand equals supply, maximizing profit. The revenue and cost functions help derive average and marginal measures.

The curves visually represent how these functions intersect at equilibrium. Elasticity of demand at equilibrium denotes the sensitivity of quantity demanded concerning price changes. The price markup highlights the firm's ability to set prices above marginal cost due to factors like market power or product differentiation, allowing for profit generation.