micro quizz7 - A. Algebra and mathematical analysis Problem...

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A. Algebra and mathematical analysis Problem 1. Let the national- income model be : 0 0 G I C Y + + = ; ) ( . T Y C - + = 8 0 20 ; Y T 2 0 5 . + = . Find the equilibrium levels Y , C and T in terms of 0 I and G 0 . Problem 2 . The demand and supply functions of a single market are as followed 2 2 6 0 3 2 4 0 2 48 P P Q P P Q s d . ; . + + - = - - = a) Express the market equilibrium condition of this market in the form of a quadratic equation of variable P . b) Find the equilibrium price and the equilibrium quantity P , Q . Problem 3 . Given the input – coefficient matrix and the final-demand vector: = . . . . . . . . . . 2 0 4 0 4 0 3 0 1 0 1 0 2 0 2 0 1 0 A and = 60 40 100 d . a) Find the technology matrix T and it’s determinant . . b) Write down the specific input-output matrix equation for this model and find the “correct” output levels for the three industries. Problem 4. Given an average cost function AC= Q Q + + 20 400 a) Find the total cost function and the fixed cost. b) Find the minimum average cost output level. Problem 5. Given a consumption function in term of the income Y : Y C 6 0 200 . . + = a) Find the marginal propensity to consume and explain it’s economic meaning. b) Find the elasticity of consume with respect to the income level when Y=$1,000 and explain the economic meaning of the obtained value . Problem 6 .A single product monopolistic firm supplies it’s products to two separate markets .The demand functions in the first and second market are respectively : 1 1 620 P Q d - = ; 2 2 700 P Q d - = and the total cost function : 2 60 50 Q Q C + + = . Find the output level and the quantities supplied to each market in order to maximize it’s profit. Problem 7 . a)A single -product firm faces the marginal revenue function and marginal cost function as following: Q MR 2 340 - = ; MC = 100+ Q
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It is known that the fixed cost of the firm is 500. a) Find the total revenue and total cost function. b) Find the profit function and maximum profit output level. Problem 8 . a) Find the present value of the perpetual cash flow A= $2,000 if the discount rate r = 0.08. b) Evaluate the following improper integral : I= + 1 2 dx x x ln B. Probability Problem 9 . A person intends to invest in a stock market . There are two choices: stock A or stock B .In the case he invests in stock A , he obtains a return of 25 percent if the economy is strong and ( -10 ) percent if the economy is weak. In the case of stock B , he obtains the return of 15 percent if economy is strong and 10 percent if the economy is weak. He believes that the that the economy is strong with the probability 0.60 and weak with the probability 0.40. He wants to invest in the stock which has higher expected return. Which stock
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micro quizz7 - A. Algebra and mathematical analysis Problem...

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