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 ABC's 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 firm's 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, demonstrated by the decreasing coefficient c in the MC function, but c still remains higher than 1 (the slope of MC curve is smaller than before it does not change significantly). 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 both short run rather than keeping doing the same business as he has been doing.

Requirements:

Make sure you explain your argument exhaustively about the effects of product quality upgrade on the change in profitability of the firm, whether those positive effects of the new equipment definitely bring higher profit for the firm, what factors the profitability depend on; based on the argument, conclude your recommendation whether the owner of ABC should invest in the new equipment for product quality upgrade or not.

Your discussion should reflect the concepts of competitive market structures, the framework of profit maximization in competitive markets (topics 4 and 5) that you have learnt in the course. Furthermore, you should note that price elasticity of demand and production costs (topics 2 and 3) are the two relevant reasonings for your discussion.

Hint: A suggestion of high-level structure of your discussion with the firm's owner is as below.

Question 1: DISCUSS THE SHORT-RUN PROFITABILITY OF THE FIRM IN THE CASE OF NOT UPGRADING THE PRODUCT QUALITY.

What is the market structure and the firm's price setting? How does the firm generate marginal revenue given the price setting? Facing the problem of diminishing marginal returns (DMR), what is the cost structure the firm currently has, i.e. the relative proportion of labor and capital in total cost? What are the slopes of marginal cost and average costs with the cost structure? What is the firm's output decision given the price setting and the production cost condition? What is the associated short-run profit for the firm in this business setting?

Question 2: DISCUSS THE SHORT-RUN PROFITABILITY OF THE FIRM IN THE CASE OF INVESTING IN THE NEW EQUIPMENT AND UPGRADING THE PRODUCT QUALITY.

What is the market structure and the firm's price setting? How does the firm generate marginal revenue given the price setting? Assuming the cost of buying new equipment has minimal change in the firm's cost structure, with the positive effect of the new technology of the equipment, measuring the labor productivity and mitigating the problem of DMR, would the firm's marginal cost and average costs be higher or lower than before? What is the firm's output level decision and associated short-run profit in the new business setting?

Question 3: 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.