Market demand and supply in a perfectly competitive market are given as Qd = 100 - 2P and Qs = 40 + P, respectively. A firm in the market has the cost function, TC = 1/3Q3 - 3.5Q2 + 26Q + 10, where TC is the total cost and Q is output.
a- Graph demand and supply in the market.
b- Find market price and quantity.
c- What is the optimum level of output for the firm.
d- Find the profit of the firm.
e- Prove that for the demand function given above price elasticity of the demand equals to one in the middle of the demand curve, is greater than one at higher prices, and is less than one at lower prices.