Question

The Mikado miniature camera company found that consumers were willing to pay P-02x+80dollars for x cameras and producers were willing to sell x cameras for P-01xx+40dollars. Sketch the graph of both functions. (Carefully and meaningfully label the x and y axes, the y intereepts, and each function.) What is the equilibrium price? What is the equilibrium quantity? Shade the region in the above graph the represents the Producer's Surplus. Give, and solve, (via calculator), the definite integral the represents the Producer's Surplus. Give the definite integral that represents the Consumers Surplus. Use the Fundamental Theorem of Calculus to find the Consumers' Surplus

Answer 1

100- (0, 80) (10, 60) -50- (0, 40) |(20, 0) 20 10 4 1 -0.2х + 80 2 0.1x x40 П

In the graph y-axis represent the price and x -axis represent the number of cameras produced.

From the graph we see that:

1. The equilibrium price is the price at intersection between the two graphs on positive x-axis which is $60.

2. The equilibrium quantity is 10 cameras.

3. The region for producers surplus is th region shaded with black in the graph:

4. The producers surplus is given by:

100- (0, 80) |(10, 60) -50- |(0, 40) |(20, 0) 20 10 4 1 -0.2х + 80 2 0.1x x40 П

10 (0.2x280) (0.12 40))dr 250

The producers surplus is 250.