Answer, the attached questions precisely.

1) Suppose that Lisa consumes two goods, bread (represented by x) and cheese (represented by y). Suppose that your utility function is: U(x.y) = xy 4 [1]. Assume the time period is I week. The marginal utility functons for bread and cheese are respectively: MU,(x,y) =()" [2] and MU,(x,y) = ()" [3] a) Find the equations of 3 of Lisa's indifference curves (IC) for which the value of utility is held constant at respectively U = 10,U = 25, and U = 50. b) In Table 1, for each IC, plot the y values corresponding to the x-values. Now, use the table values to plot each of the three ICs on Fig. 1 (see table and graph grid at end of the assignment). On your graph, draw an arrow to indicate the direction of increasing utility. c) Use the functions [2] and [3] to find the equation of the marginal rate of substitution (MRS) in terms of the amount of the y-goods Lisa is willing to give up to get an additional "small unit" of x-goods. Le. the rate at which Lisa is willing to exchange y-goods for x-goods starting at a given bundle (x.y). Note: We can think of this MRS as Lisa's marginal benefit (MB) of bread measured in units of cheeses. d) On the IC at which O = 25, label the bundle A = (25. 25) and draw a tangent line and use the formula, MRS(x.y) = - slope tangent at the bundle = - (rise)run. Repeat for two other spaced out points on the IC [one to the right of A (call it B) and one to the left of A (call it C)]. e) Suppose that Lisa's weekly food budget is M = $100 and the price of bread (p,) is $1/unit while the price of cheese is py = $3/unit. Write down an equation for Lisa's budget line and rearrange it to get y as a function of x. Plot your budget line on Fig. I and label it. Also, label Lisa's feasible and non-feasible sets of consumption bundles by light shading in different colours.1. Diamond-Mortensen-Pissarides with on-the-job search Time: Discrete, infinite horizon Demography: A mass of 1 of workers with infinite lives. There is a large mass of firms who create individual and identical vacancies. The number of vacancies, v, is controlled by free-entry. Preferences: Workers and firms are risk neutral (i.e. u(r) = r). The common discount rate is r. The value of leisure for workers is b. The cost of holding a vacancy for firms is a utils per period. Productive Technology: A firm matched to a worker produces p units of the consump- tion good per period. With probability A each period, jobs (filled or vacant) experience a catastrophic productivity shock and the job is destroyed. Matching Technology: In this arrangement, workers are always in the market. Whether they have a job or not does not stop them getting another job. As they can only have one job at a time if an employed worker meets a firm with a vacancy, the worker quits the current job and switches employment to the new firm. Firms cannot commit to paying a higher wage than the current firm. (Wages are determined by Nash bargaining and symmetry will mean they all pay the same wage.) With probability m() each period workers encounter vacancies where again v is the mass of vacancies. The function m(.) is increasing concave and m(v) um'(v). The rate at which vacancies encounter workers is then m(v)/v which is decreasing in v. (Assume that job destruction and matching are mutually exclusive so m() + ) > 0) equilibrium exist? Explain. (e) Obtain an expression for steady-state unemployment. (f) How does unemployment change with the separation rate, A? Briefly explain.1. Given that 210 out of a sample of 615 recent college graduates indicated they had graduated from college in four years, what will the sample proportion (or p) be? Please compute this value below and round your answer to three decimal places. a. To be able to conduct a hypothesis test, we will now need to compute a test statistic (using the following formula). Please attempt to compute this test statistic below, showing as much work as you can. I p - p Z = p (1 - p) n b. Remember that as part of the process of conducting a hypothesis test, we need to find what's called a probability value, or a p-value for short. This p-value value tells us something about how likely it would be to observe results at least as extreme as what we observed, if the null hypothesis is really true. Based on the test statistic you calculated to answer Question 6, what should the p-value be equal to? Please use Table B to find this p-value. (Hint: Don't forget that since a p-value is a probability, you need to now take the percentile you get from Table B and divide it by 100 to convert it to a probability). We determine if we should reject the null hypothesis based on how the p-value compares to our chosen significance level. If we assume here that we are using a significance level (or an alpha level) of 0.05, should we reject the null hypothesis or fail to reject the null hypothesis? Please explain the reason for your answer. d. If a larger significance level had been chosen-like 0.10-would you have made a different decision (compared to the decision you explained in your answer to Question 8) about whether to reject or fail to reject the null hypothesis? Please explain. C. If a smaller significance level had been chosen-like 0.01-would you have made a different decision (compared to the decision you explained in your answer to Question 8) about whether to reject or fail to reject the null hypothesis? Please explain.Minnie consumes two goods. I. and .tg and her utilityr function is it = [I] + 2:}(172 +4) a} {5 points} Find her Marshall demands \"(pl \"113, m) andxpl ,pg, m) using the Lagrangian function. h} [3 points} Express the indirect utility function v(p1.p2, m) and simplify the expression. c} {3 points} Derive the expenditure function 071,132, it) from indirect utility funcon. d} [3 points) Derive the Hicksian demands it 1 (p; , pg, 11) and 13031 1p: , it) using the Shepherd's lemme. e} [6 points} Assume that Minnie's budget is $120 and x1 costs $10 while .172 costs $5. Now suppose that the price of :2 increases to $20. calculate the substitution and income effect due to this price change for both commodities using the Hicksian decomposition