In big cities, there are many small businesses producing and selling necessity goods and services (such as laundry services, hair salons, garage services, restaurants, fruit shops, bakeries, etc.) to serve the local citizens. The common problem of all the small businesses in the cities is that their products look quite similar and they are likely to engage in aggressive price competition. Each firm currently sets the same price level with each other. The demand function format is P(Q) = a, with a is a constant number (i.e. price level remains at a regardless any change in Q). A small firm ABC is considering whether it should upgrade its product quality to compete with its rivals. The owner of a shop ABC comes to know a new kind of equipment that helps to reduce the product errors and enhance the typical product quality attributes better suiting customers orders. Most of ABCs customers said they would be willing to pay more than the current price for the enhanced quality attributes while the other customers said they are happy at current price level. The demand function is now down-ward sloping: P(Q) = A -b*Q, with A and b as constant numbers (i.e. price changes with respect to Q) and b is smaller than 1, and please note "A" of this demand function after quality upgrade is now different from "a" before the quality upgrade. Additionally, the firms marginal cost is MC(Q) = c*Q, with c > 1, and c is a constant number (i.e. the firm is currently facing diminishing marginal returns, MC increases with respect to Q). The business owner finds that the new equipment brings another benefit for the firm to program and monitor workers production time and hence helps the firm to determine optimal uses of labor and would mitigate the problem of diminishing marginal returns the firm currently has. It would help the marginal cost decreases, but c still remains constant, demonstrated by movement downward along MC function. Assuming the cost of buying the equipment minimally affects to fixed capital of the shop business. Average total cost varies accordingly to the marginal cost. The owner of ABC believes that investing in the equipment for the product quality upgrade would bring higher profits in short run rather than keeping doing the same business as he has been doing.

PART : COMPARE THE SHORT-RUN PROFITABILITY OF THE FIRM WITH AND WITHOUT PRODUCT QUALITY UPGRADE.

Particularly, compare the optimal output levels between two cases, then compare price levels the firm can set, and compare the production costs with and without the quality upgrade. From the comparison of the profitability, conclude whether buying the new equipment definitely bring the firm higher profit, what factors the profitability depend on and conclude your recommendation whether the owner of ABC should invest in the new equipment for product quality upgrade or not. And draw Graph illustration of short-run profitability in two cases with and without investment in product differentiation