A consulting company estimated market demand and supply in a perfectly competitive industry and obtained the following results: $$Q _ { \mathrm { d } } = 25,000 - 5,000 P + 25 M$$ $$Q _ { s } = 240,000 + 5,000 P - 2,000 P _ { J }$$ where P is price,M is income,and $$P _ { I }$$ is the price of a key input.The forecasts for the next year are $$\hat { M }$$ = $15,000 and $\hat { P } _ { I }$ = $20.Average variable cost is estimated to be $A V C = 14 - 0.008 Q + 0.000002 Q ^ { 2 }$ Total fixed cost will be $6,000 next year.What is the price forecast for next year?

Question

Quizplus · Accepted Answer

To forecast the price, we need to set the demand equal to supply and solve for P. Given $\hat{M} = 15000$ and $\hat{P_I} = 20$, we substitute these values into the demand and supply equations:$$Q_d = 25,000 - 5,000P + 25(15,000)$$$$Q_s = 240,000 + 5,000P - 2,000(20)$$Simplifying:$$Q_d = 25,000 - 5,000P + 375,000$$$$Q_s = 240,000 + 5,000P - 40,000$$Further simplifying:$$Q_d = 400,000 - 5,000P$$$$Q_s = 200,000 + 5,000P$$Setting $Q_d = Q_s$:$$400,000 - 5,000P = 200,000 + 5,000P$$Solving for P:$$200,000 = 10,000P$$$$P = 20$$Therefore, the price forecast for next year is $20.

A Consulting Company Estimated Market Demand and Supply in a Perfectly