Alice has utility from hours of TV and hours of movies given by U (t, m) =5t + 4m.(a) Obtain the equation of the indifference curve for the utility level U = 100 (set min the vertical axis).(b) Draw three indifference curves for Alice, and label the levels of utility that theycorrespond to (you can choose the utility levels that you want). Set m in thevertical axis and t in the horizontal axis.(c) What is Alice’s marginal rate of substitution M RS? Hint: Adopt the conventionof treating t as x and m as y.(d) If Alice’s income is $50, and the price of movies is $2 per hour and the price ofTV is $1 per hour, how much of each will she consume?(e) What if the price of movies is $1 per hour and TV is $2 per hour?(f) Obtain the equation of the indifference curve for the utility level U = 20 (set min the vertical axis). Is this indifference curve steeper than the indifference curveyou derived in part (a)? Explain.3

Johnathan’s utility function isU(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)

A consumer has an income of $10,000 to spend on two goods, X and Y, where the price of good X is $500 per unit, and the price of good Y is $1 per unit. The marginal rate of substitution is given by the formula Y/X. How many units of good Y does this consumer optimally consume?

Fill in the spaces:a. Along an indifference curve ____________ is constant.b. The rate at which a consumer is willing to substitute one good for another, holding utilityconstant, is given by the ____________ of an indifference curve. This rate is called the_________________________________.c. If at a given combination of X and Y, a consumer’s marginal rate of substitution is 4, thismeans that the consumer is willing to give up ______ units of Y for another X or ______units of X for another Y.d. If a consumer is choosing the levels of goods X and Y in order to maximize utility with agiven budget the _________ equals the ____________ ratio of the goods.e. The rate at which a consumer can substitute one good for another in the market is given bythe ______ of the budget line and is equal to the __________ratio of the two goods

a) Assume Jamaal can work up to 60 hours per week at a rate of$10per hour, and that because of a government subsidy, Jamaal has$200in unearned income per week. Draw Jamaal's budget constraint showing how much Leisure (L) and Consumption (Y) he can have. Label both axes with values and titles. Call this Line A. Assume that Jamaal is a leisure lover and at his preferred bundle he works for 10 hours. Label this point A and draw an indifference curve for this bundle labeledU A​ . How much does he earn? (b) Now assume that the cost of child care for Jamaal's daughter is$100per week which he pays only if he works any hours>0. Re-draw his budget constraint on the same graph and label it Line B. What effect will this cost likely have on the amount of labor Jamaal supplies assuming both consumption and leisure are normal goods? Talk about this in terms of income and substitution effects. If Jamaal preferred to work 10 hours in the case of no child care costs, how many hours do you think he will work now? (c) Now assume that Jamaal's employer is willing to pay$3.33of Jamaal's child care expenses for every hour he works, but only if he works 30 hours or more. Now re-draw Jamaal's budget constraint and label it clearly as Line C. Given what you drew for your previous indifference curves, how do you think this will affect Jamaal's consumption of Leisure and Market Goods? Will he work more, less or the same? Explain why.Thanks in advance!Skip questionStart SolvingExitExitQnA

Jack consumes only Bread (good x) and Cheese (good y). His utility function is given byU (x, y) = ln(x) + ln(y)(a) Find Jack’s marginal rate of substitution (MRS) at bundle (x, y).(b) The price of good x is $6 and the price of good y is $3. Jack has an income of $120. Findhis utility-maximising consumption bundle.(c) Calculate Jack’s utility from the bundle you have found in part (b). (You can leave youranswer expressed in logarithm.).(d) In a graph with the quantity of x on the x-axis and the quantity of y on the y-axis, drawJack’s budget line, clearly marking the intercepts and the utility maximising bundle youhave solved in part (b) (call it bundle A). Also sketch an indifference curve passing throughbundle A.(e) Now the price of good y increases to $6 while the price of good x remains at $6. Jack’sincome remains at $120. Calculate his new utility-maximising consumption bundle.(f) On the diagram you have drawn for part (d), draw Jack’s new budget line, clearly markingthe intercepts and the new optimal bundle you have solved in part (e) (call it bundle B).Also sketch an indifference curve passing through bundle B.(g) Find the minimal expenditure required for Jack to achieve his original utility level (i.e.,your answer to part (c)) under the new prices. As you are finding this minimal expenditure,solve for the expenditure-minimising bundle that achieves the original utility level underthe new prices.(h) On the diagram you have drawn for parts (d) and (f), draw the budget line associatedwith the minimal expenditure you have solved in part (g), clearly marking the interceptsand the expenditure-minimising bundle you have solved in part (e) (call this bundle H).