3. 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.
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- 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?1. Assume well behaved preferences for a consumer. If total income goes up, ceteris paribus what would be the impact on the Budget line? 2. Assume well behaved preferences for a consumer. If total price of good on Y axis goes up, ceteris paribus what would be the impact on the Budget line? 3. Differentiate between the concept of Income effect and Substitution effect in Price Decomposition3. Susan has the following utility function U(x,y) = xy, where x represents food and y represents other goods. Susan has £20 (budget m) to spend on these two goods. Suppose that the initial price of x (Px) is £1 per unit, and that of y (Py) is £1 per unit. Note that MUx=y and MUy=x. (i) How many units of x and y will Susan purchase? Assuming that Px varies and m and Py stay constant at the values £20 and £2, respectively, what is the individual demand function for x? (ii) What are the characteristics of the individual demand function for x? What is its aggregate counterpart, and what is its economic importance?
- 1.a Assume that a person’s utility function is given by the following function: ??=3?^(2/3)?^(1/3) Assume also that the price of X is £3, and the price of Y is £3 and that the budget is £45. What is the optimal amount of goods X and Y that should be purchased with this budget? b) Assume now that the price of good X is PD, while all other conditions remain the same. Find the optimal amount of good X that should be purchased for a generic price PD. In other words, find the individual demand function for good X. 1.b Assume now that the price of good X is PD, while all other conditions remain the same. Find the optimal amount of good X that should be purchased for a generic price PD. In other words, find the individual demand function for good X.3. Tony is throwing a party at his Fraternity and is trying to choose what booze to buy. A bottle of vodka has three times the alcohol as a six-pack of beer. Assume that Tony only cares about the total amount of alcohol in his basket. (use vodka on the X-axis and beer measured in six-pack on the Y-axis) a) Devise a utility function to represent these preferences. b) Suppose a bottle of vodka costs $40, a six-pack of beer costs $10, and the budget is $200. Write the budget constraint. c) Solve Tony's utility maximization problem and find the optimal combination. d) Suppose that a bottle of vodka cost has increased to $50. What will be his new optimal combination?1. Problems and Applications Q1 1. Effect on Budget Constraint 2. Effect on Optimum Maya divides her income between coffee and croissants (both of which are normal goods). Exceptionally good weather conditions in Brazil cause a large decrease in the price of coffee in the United States. Coffee On the following graph, show the effect of the good weather conditions on Maya's budget constraint (BC). STEP: 1 of 2 BC Croissants لمدة
- 1 Alice has a monthly lunch budget of 360 dollars which she spends on either burgers (B) or pizza (Z). The price of each pizza is 16. dollars and the price of each burger is 8 dollars. Alice's utility is given by: u(B, Z) = B'/2 +4Z!/2 + 47!/2 a) Find Alice's budget constraint. Set up the Lagrangian and find her optimal consumption. What is her new consumption if the price of burgers becomes 16 dollars?1. Use the budget constraint P_X + P_Y = M, thinking of good X as a food item and good Y x as other goods. Present an analysis where an increase in price of the food item causes the consumer to buy less food, demonstrating the "law of demand." b. Then, present a second analysis where an increase in the price of the food item causes the consumer to buy more of the food item, which is the Giffen Good case. Finally, identify two food items, one which you think fits the first case and one which you think fits the second case.2a) Sompa's utility function for strawberries and grapes is given by U (S, G) =10s?G'. Where S represents strawberries and G represents grapes. i. Write down Sompa's budget constraint. ii. What combination of strawberries and grapes maximises Sompa's utility if her income is GHC200, the price of strawberries is GHC 5per unit and the price of grapes is GHC 10 per unit? ii. What is Sompa's total utility (satisfaction)? iv. If the price of strawberries increases to GHC15 per unit and the price of grapes and Sompa's income remain the same, discuss briefly what Sompa will have to do to maximize her satisfaction. b) Supposing strawberries was a giffen good, derive the demand curve for strawberries with this increase in price. c) Explain the notion that "on the basis of price changes goods can be classified into normal and giffen, and on the basis of income changes, goods can be classified into normal and inferior".
- 2. Utility function: U(X,Y)= 2XY* Budget Constraint: 2X +4Y = 80 a. Calculate the utility maximizing amount of X and Y.Draw YOUR indifference curve for the consumption of two goods (you pick the goods – be creative!) Make sure to include labels. Why did you choose these two goods? Why do you view these as being a tradeoff? Carefully explain why the indifference curve has the shape you created. (Hint: Discuss the slope. What it means and how it changes) Determine a budget that will be allocated towards your consumption of these two goods. Given the budget, prices for the goods, and your preferences, how will you find the utility-maximizing combination? Give an intuitive answer as well as a graphical answer (make sure to label the graph accordingly).Suppose you have $100 to spend on Skittles and M&Ms. The price of Skittles is $5.00 and the price of M&Msis $1.00.(a) Write the budget constraint and draw the budget constraint on a graph that has M&Ms on the verticalaxis. (b) Assuming you spend all of your money on skittles and M&Ms. If you bought 10 M&Ms how manySkittles did you purchase? (c) Suppose the price of skittles increases from $5.00 to $6.00. Rewrite the budget constrain and draw thenew budget line, including and indicating intercepts and the slopes. (d) Suppose the price of Skittles drops from $5.00 to $1.00. You are limited to only a maximum of 75skittles. Draw this new budget constraint on the same graph from your answers in part (a) and (c).