Consider a consumer with income M, who can buy good x₁ at price p₁ per unit and can buy good 2 at price p2 per unit. Consider a budget constraint diagram for this consumer, with quantity of good ₁ measured along the horizontal axis and quantity of good 2 measured along the vertical axis. If p₁increases and M increases (though not necessarily by the same percentage), while p2 remains unchanged, which of the following changes to the consumer's budget set definitely occur? O The budget line slope becomes steeper The budget set becomes strictly larger The budget line slope becomes flatter None of these changes necessarily occur O The budget set becomes strictly smaller

Assume that you are on an island where there are only two commodities—coconuts and pineapples—and you can spend your income only on these two foods. If the price of coconuts is Pc and the price of pineapples is Pp and your income is I, draw a budget constraint, carefully labelling the points on the two axes and where the attainable and unattainable portions of consumption are. Note: you can choose any Pc and Pp that you like—they do not have to be equal. What is the slope of this budget constraint? What is the economic interpretation of the slope? Now, let’s bring a little more structure to this diagram. Let I=£200, Pc=£1 per coconut and Pp=£2 per pineapple. Draw a new diagram using these numbers. Consider these questions: How many coconuts can you buy if you do not buy any pineapples? How many pineapples can you buy if you do not buy any coconuts? What is the slope and what economic information does it give us? Show the point of 100 coconuts and 100 pineapples on your diagram. Can…

1) Max chooses to purchase movie tickets and restaurant meals every week with his $100. If the price of a movie ticket is $20 and the price of a restaurant meal is $25, then the slope of his budget constraint will be, a) 1/5 b) -1/5 c) 4/5 d) -4/5   2) Marginal rate of substitution(MRS) is the rate at which consumer is willing to trade one good for another. It must be true that: a) MRS is the slope of an indifference curve in reference to a particular bundle of goods. b) MRS is not the same along an indifference curve that is of usual shape. c) MRS is same along an indifference curve that is of usual shape. d) Both a) and b).

1 FOOD STAMPS Consider a person who has $750 per month in income and has preferences for food (F) and all other goods (X) represented by a utility function, U(F, X) = F⁰.2 X0.8. To simplify analysis, let's assume that both the price of food and the price of all other goods is $1 per unit such that F and X represent expenditure on food and all other goods, respectively. a. Set up a Lagrangian and derive the consumer's demand functions for food and all other goods. As you are solving, make sure you can explain each step in words. b. Now solve for the demand functions using the "substitution approach" whereby we sub- stitute the constraint directly into the objective function. Show that the resulting demand functions are the same as in part (a). c. What is the consumer's optimal bundle given the prices and income? How much utility does the consumer derive from this bundle? Now assume that the government introduces a Food Stamps program that gives this con- sumer $250 that she can only…

Describe and graph your own example of a budget constraint using two goods (don’t forget to label your axes). In your example, make sure to state what the budget is, the price of the two goods, what the slope of the budget constraint equals (make sure to include the correct sign), and interpret what the slope represents.

A consumer has a budget of £12 to split between two goods: good 1 has a price of 2, good 2 has a price of 3. Write the consumer’s budget constraint algebraically. Convert this budget constraint into the formula for the budget line. Show this line on a suitably labelled graph. The consumer’s budget increases to £24. Show the effect of this change graphically.  A consumer dislikes good 1, and dislikes good 2. Show these preferences on a suitably labelled graph with an indifference curve. Label the graph: which areas would be preferred to those on the line?

Plot each of the bundles from parts A – C on a graph that measures avocadoes on the horizontal axis and loaves of bread on the vertical axis, connect the dots to find Matt’s budget constraint. Show what happens to the budget constraint if his income falls to $100, (prices do not change). Show what happens to the budget constraint if price of avocado rises to Pa = $2 per avocado, (income and price of loaves of bread did not change).

Sarah likes basketball games and going to movies. Every month he has $480 to spend on the two activities. Ticket price of a basketball game is $15 and price of a ticket to movies is 12$. Write the budget constraint equation and draw the budget constraint for Sarah.

Suppose you are given the following information for a particular individualconsuming two goods, a and b: Pa = $5, Pb = $6, MUa = 100, MUb = 200, and income (m) = $200.a) Sketch the budget set. What is the slope of the Budget Line? What are maximal possibleconsumptions of a and b?b) What is the MRSab for the two goods?c) Is this person maximizing her utility? How can you tell?d) Should she consume more of good a or of b? Explain.e) Why can’t you tell what her optimal bundle is? Explain.

Sonia likes cupcakes and tea. She has Rs.100 to spend on cupcakes and tea; cupcakes cost Rs.20 each, and cups of tea cost Rs.10 each. Sketch her budget constraint on a graph with cupcakes on the horizontal axis and cups of tea on the vertical axis. Sonia also has a calorie constraint: she can only consume 800 calories, and each cupcake has 200 calories, while tea has no calories. On your graph, sketch in Sonias calorie constraint and indicate her budget set - the set of feasible combinations of cupcakes and tea given her two constraints. Label all the kinks of Sonias budget set with their coordinates.