1. Briefly explain the difference between the following a. Increasing returns to scale, Decreasing returns to scale and Constant returns to scale b. Marginal cost, Average variable cost and Average cost c. Shut down point and breakeven point 2. With the help of calculus, prove the following. a. The condition for cost minimizing combination of laborand capital is r MPK MPL C. The condition for profit maximization is MC= MR 3. A firm's short run cost function is C(a)- 150g-42+0.4q3+ 275. Determine the fixed cost F; the average variable cost, AVC; Average Fixed Cost, AFC; Average Cost, AC, and the Marginal Cost, MC A firm's profit function is given by T) TRa) - C(a) where TR is Total Revenue and C is total cost. If the profit function is n)-150q-(150+30q+ 10q2), what is the output q that maximizes the firm's profit? What is the firm's revenue, variable cost, and profit? Should the firm operate or shut down in the short run? (Hint: What is the condition for profit maximization?)