Question

This problem focuses on the interaction of the corporate profits tax with firms' investment decisions. a. Suppose (contrary to fact) that profits were defined for tax purposes as what we have called pure economic profits. How would a tax on such profits affect investment decisions? b. In fact, profits are defined for tax purposes as \\[ \pi^{\prime}=p q-w l-\text { depreciation } \\] where depreciation is determined by governmental and industry guidelines that seek to allocate a machine's costs over its "useful" lifetime. If depreciation were equal to actual physical deterioration and if a firm were in longrun competitive equilibrium, how would a tax on \(\pi^{\prime}\) affect the firm's choice of capital inputs? c. Given the conditions of part (b), describe how capital usage would be affected by adoption of "accelerated depreciation" policies, which specify depreciation rates in excess of physical deterioration early in a machine's life but much lower depreciation rates as the machine ages. d. Under the conditions of part (c), how might a decrease in the corporate profits tax affect capital usage?

Short answer

Answer: A tax on pure economic profit serves as a fixed cost to the firm, reducing its overall profitability. However, as long as the firm is making a positive pure economic profit after the taxes, it will have the financial capacity to invest. As a result, a tax on pure economic profit might not directly affect a firm's investment decisions but could affect the overall profitability and funds available for reinvestment.

Step-by-step solution

Pure economic profit is the difference between the total revenue a firm receives and its opportunity costs. It represents the profit a firm has after considering all the direct and indirect costs, including normal profit. #Step 2: Explain the tax on pure economic profit and its impact on investment decisions#

If profits were defined for tax purposes as pure economic profits, a tax on such profits would act as a fixed cost to the firm and reduces its overall profitability. However, as long as the firm is making a positive pure economic profit after the taxes, it will have the financial capacity to invest. As a result, a tax on pure economic profit might not directly affect a firm's investment decisions but could affect the overall profitability and funds available for reinvestment. #b. Effect of tax on actual profit considering depreciation# #Step 1: Define the given equation for profits#

Profits are given by the equation: \\[\pi^{\prime}=p q-w l-\text { depreciation } \\]Here, \\(\pi^{\prime}\\) is the profit, \\(p\\) is the price of output, \\(q\\) is the quantity of output, \\(w\\) is the wage rate, \\(l\\) is the labor input, and depreciation refers to the loss in value of the capital over time. #Step 2: Analyze the effect of a tax on actual profit with depreciation on capital inputs#

If depreciation were equal to actual physical deterioration and the firm were in long-run competitive equilibrium, a tax on \\(\pi^{\prime}\\) would not affect the firm's choice of capital inputs. This is because, in a long-run competitive equilibrium, the firm's profits are already reduced to zero, leaving no additional funds to invest in capital. #c. Effect of adopting accelerated depreciation policies# #Step 1: Describe accelerated depreciation policies#

Accelerated depreciation policies specify depreciation rates in excess of physical deterioration early in a machine's life but much lower depreciation rates as the machine ages. It means that the value of the capital will decrease more rapidly during the early years of use and would allow the firm to report lower taxable profits during this period. #Step 2: Analyze the effect of accelerated depreciation policies on capital usage#

Given the conditions of part (b), adopting accelerated depreciation policies would lead to a higher depreciation rate early in the machine's life and result in lower taxable profits. This could provide an incentive for firms to invest in newer capital assets, as they can have higher depreciation rates and hence, lower taxable profits in the beginning. Hence, it could result in an increase in capital usage. #d. Effect of a decrease in the corporate profits tax on capital usage# #Step 1: Analyze the impact of a decrease in the corporate profits tax#

Under the conditions of part (c), a decrease in the corporate profits tax would mean that the tax burden on firms is reduced. This could potentially lead to increased profitability for firms and more funds available for investment. #Step 2: Determine the effect on capital usage#

With additional funds available due to the decrease in corporate profits tax, firms might be more likely to invest in capital assets, increasing capital usage. However, the adoption of accelerated depreciation policies might still be in place, providing an incentive for firms to invest in new capital assets with higher depreciation rates early in their life, as it would help in reducing taxable profits. Overall, a decrease in corporate profits tax under the conditions of part (c) could lead to an increase in capital usage.