[ U=q_{\frac{1}{2}}^{\frac{1}{2}} q_{v}^{\frac{1}{2}} . \] We showed earlier in the course that maximizing this utility subject to a budget con-straint yields the result \[ \frac{q_{y}}{q_{x}}=\frac{P_{x}}{P_{y}} \] You may use this result below. This world also has a production possibilities frontier (PPF) whose equation is \[ 800=q_{x}^{2}+4 q_{v}^{2} \] (a) Calculate the Marginal Rate of Transformation (MRT). (b) Give the equation relating MRT and prices. (c) Calculateq z​ ,q y​ andP y​ P z​ ​ . (d) Draw the PPF, labelling three points with numerical values. Arithmetic hint:800​ =28.3, 200​ =14.1.) (e) Show on the graph how the price ratioP y​ P z​ ​ is determined. Please add appropriate labels.Skip questionStart SolvingExitExitQnA

Consider the following budget constraint. \[ \mathrm{I}=\mathrm{PB}^{*} \mathrm{~B}^{*}+\mathrm{PT}^{*}{ }^{*} \mathrm{~T} \] and Utility Function \[ U(x, y)=\left(6 T^{5}+4 B^{5}\right)^{1 / 5} \] Where

U(x, y) = (3x + 2y)2 .The price of x is px = $10 per unit and his income is $200.(a) Obtain the equation of Johnathan’s indifference curve for the utility level U = 100. Drawthis indifference curve. (2 marks)(b) The price of y is py = $8 per unit. Obtain the marginal rate of substitution (MRS) and theequation of the budget line. Using a graph, find Johnathan’s optimal consumption bundle.In this graph, show the budget line, the optimal bundle, and the corresponding indifferencecurve. Make sure to label carefully all the curves. (3 marks)(c) Suppose that the price of y drops to py = $6 per unit (the price of x remains the same,at px = $10 per unit, and the income remains the same). Obtain the equation of the newbudget line. Using a new graph, find Johnathan’s optimal bundle with this new price. Inthis graph, show Johnathan’s new budget line, new optimal bundle, and the correspondingindifference curve. Make sure to label carefully all the curves. (3 marks)(d) Now suppose that the price of y is py = $8 per unit if Johnathan buys less than 10 units ofthis product, and py = $6 per unit if he buys 10 units of y or more (as an example, 20 unitsof y would cost $120). Assume that the price of x remains the same, at px = $10 per unit.Derive the equation of the budget line and draw it in a separate graph. (3 marks)(e) Using a new graph, find the optimal bundle(s) for the problem in part (d). In this new graph,show the budget line, the optimal bundle and corresponding indifference curve. Make sureto label carefully all the curves. (3 marks)

Consider an economy with two consumers, each with a marginal benefit for a public good ofMB = 20 – (q/2). If the marginal cost of provision is $16 per unit, what is the efficient level of output?

A profit-maximising firm in a monopolistic competition setup will seek to produce the quantity Q where (X), and charge the price indicated by the firm’s (Y) curve at quantity Q. Identify X and Y.X = marginal cost equals marginal revenue; Y = marginal cost X = average cost is more than average revenue; Y = average total cost X = marginal cost equals marginal revenue; Y = demand X = average cost is more than average revenue; Y = demand

Consider a production possibilities frontier (PPF) with Good X on the horizontal axis and Good Y on the vertical axis. The slope of the PPF tells us the _____ of producing one additional unit of Good X.Multiple choice question.profitabilitytotal costaverage costopportunity cost