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3. (20 points) Principal-Agent The probability of winning a soccer match is determined in part by the level of effort of the players. Assume that the probability of winning a match is given by the function: Pm (e) = 26 82 Where 6 is the level of effort by the average player. 6 is continuous and bounded by the [0, 1] interval. If a team wins a match; the owner of the team will earn $1, 000; if the match ends in a loss or a draw then the owner earns nothing. Then, the expected revenues are equal to R(e) = 1, OOOPw(e). For simplicity assume that the only cost for the owner is to pay the salary of 11 players. Consider the following wage arrangements: 1. w = $150 (Regardless of the outcome of the game) 2. w : 1203) 3. w = R(e) 900 The utility of the average player is given by 15(5) 2 w 2505 (a) (10 points) Find the optimal level of effort for each of the proposed wage arrangements. (b) (5 points) Find the prot level for each different contract. (c) (5 points) What's the optimal contract for the owner? Section C Calculation and Graphical Analysis (45 Marks) There are 6 questions in this section. All are compulsory. Clearly show all working and use graphical illustrations in places possible to substantiate your answer. Question 1 (15 Marks) The data of the open economy of Northland is given below. All values are in Smillions. Use the information given below and your knowledge to answer the questions that follows. Consumption: C= 10 +0.8 YD Disposable income: YD = Y-NT Government's net tax: NT = 02Y Planned investment: I = 40 Government's expenditure: G = 68 Export: X = 22 Import: 0.14Y (n) What is the value of the marginal propensity to consume? (1 Mark) (b) Calculate the value of the equilibrium level of income. (5 Marks) (c) Calculate and explain the type of government budget at the equilibrium level of income in (b) above. (3 Marks) (d) Calculate the government's expenditure multiplier. (2 Marks) (e) Calculate the recessionary gap or an inflationary gap that is created when the full employment level of potential GDP is $400 million. (1 Mark) (f) Using AD/AS model illustrate the recessionary gap or an inflationary gap that you have calculated in (c) above. (3 Marks) ECNSOlSem Semester 2, 2019 Page 6 of &Q7. The following regression output is the result of a multiple regression application in which we are interested in explaining the variation in retail price of personal computers based on three independent variables, CPU speed, RAM, and hard drive capacity. However, some of the regression output has been omitted. SUMMARY OUTPUT Regression Statistics Multiple R 0.834308875 R Square Adjusted R Square Standard Error Observations 36 ANOVA dif SS MS Regression 34335282.67 Residual Total 49327249.56 Coefficients Standard Error 1 Stat Intercept -45 95413592 730.8679496 Processor Mz 0.193481924 2.557161186 RAM 4.521583654 2.94317936 Hard Drive Capacity 174.042249 44,088963 Given this information and your knowledge of multiple regression, what percentage of variation in the dependent variable is explained by the three independent variables in the model?(22) Consider a monopoly facing the demand curve P(Q) = 100 - 2Q. The monopolist's marginal cost is MC(Q) = 10 + 5Q, and its fixed cost is FC = 100, (a) Find the quantity the monopolist produces. (b) What is the market price? (c What is producer surplus? P what is profit? (e) What is the own-price elasticity of demand at the equilibrium price
