Solve the following, please show full calculations and final answers.

3. Business Taxation and Investment A corporation is deciding how much to invest in capital to maximize the present discounted value of their profits: ;= L PDV =m + {2 (1) Where m; are profits in the first period, m; are profits in the second period, and r is the interest rate. The corporation currently has K, machines to use for production in the first period. If they invest [ in the first period they will have Ky = K, + I machines in the second period to use for production. Their profits from production net of investment in the first and second period are: 'JT'E=K?JF 7= K& Where o is the elasticity of production with respect to capital. {a) Set up the corporation's profit maximization problem and solve for the optimal KJ, I* as functions of r, K, and a. If r = .01, = .5, and K| = .1 will the corporation have pure profits in period 1 and/or period 27 (b) Suppose the government institutes a corporate income tax t profits in each period, but does not let corporations deduct investment expenses. Setup the profit maximization problem and solve for the optimal K, I"* as functions of r, , Ky, @ and t. Does the corporate income tax without investment deductions reduce investment? (c) A new administration is elected and works with congress to pass legislation to allow corporations to deduct investment expenses. Setup the profit maximization problem and solve for the optimal K, I'* as functions of r,, Ky, a and . Does the corporate income tax with investment deductions reduce investment? (d) Hoping to increase investment, the new administration proposes a one period \"tax holiday\" for corporate income. During this period the corporate income tax will be zero, while in the other period the corporate income tax will be t. Investment costs are deductible in both cases. The administration's economic advisors debate whether removing the corporate income tax in the first period or second period will lead to more investment. Setup the profit maximization problem for both cases and solve for the optimal K5, [* as functions of r,, Kj,a and t. In which period should the administration have the \"tax holiday\" to maximize investment