4 multiple part questions
Page 1 of 4 ECE103 Dr. Secrieru ECE103 Assignment #2 Handed-out March 31, 2022 Due: April 14, 2022 @23:55 EST 1. [20 marks] Miss Bates spends her money on bread and low-quality meat, and her indifference curves obey the four properties of indifference curves for ordinary goods. Suppose that, for Miss Bates, bread is a normal good. Bread costs $1.5 per loaf, and a ration of meat costs $3.5. Miss Bates has $18 a week to spend on bread and meat. a. [6 marks] Draw Miss Bates’ budget line and indifference curve that illustrates her optimal consumption bundle. [It is fine if either intercept is not an integer.] Place meat on the horizontal axis and bread on the vertical axis. Suppose her optimal consumption bundle is 3 rations of meat and 5 loaves of bread. Illustrate that bundle and draw the indifference curve, ?0, on which it lies. b. [6 marks] The price of meat increases to $4.5; the price of bread remains the same. Miss Bates now buys 2 rations of meat and 6 loaves of bread. Illustrate her new budget line and new consumption bundle on your diagram. Also draw the indifference curve, ?1, on which this bundle lies. c. [8 marks] Emma Woodhouse decides to compensate Miss Bates for the increase in the price of meat by giving her an allowance of $1.5 per week, which would give Miss Bates the same utility as she was getting before the price increase. Assume that at the new prices and with Emma’s allowance, Miss Bates consumes 1 ration of meat and 10 loaves of bread (this bundle is on indifference curve ?0). Indicate this situation on your diagram and show the income and substitution effects from this increase in the price of meat. Is meat a normal or inferior good? Justify your answer. Page 2 of 4 2. [30 marks] Cassandra allocates her income to frozen Dinners and Thai Take-out meals. The accompanying table shows her utility from the quantity of frozen Dinners or the quantity of Take-out meals. Quantity of Dinners ?? Utility from Dinners ??? Quantity of Take- out Meals ?? Utility from Take- out Meals ??? 0 0 0 0 1 50 1 50 2 80 2 95 3 100 3 135 4 115 4 170 5 125 5 207 6 130 6 225 7 139 7 241.5 8 143 8 256.5 9 145 9 270 10 146 10 275 Cassandra has ? = $150 per month to spend on Dinners and Take-out meals. The price of a frozen Dinner is ?? 0 = $9 and the price of a Take-out meal is ?? 0 = $15. a. [3 marks] Plot Cassandra’s budget line with Dinners on the horizontal axis and Take-out meals of the vertical axis. What do the horizontal and vertical intercepts represent? (Don’t worry if either of these intercepts is not an integer.) b. [4 marks] Calculate Cassandra’s marginal utility of Dinners (???) and marginal utility of Take-out meals (???). c. [4 marks] Calculate Cassandra’s marginal utility per dollar spent on Dinners, ??? ?? 0 , and her marginal utility per dollar spent on Take-out meals, ??? ?? 0 , at the given prices, i.e. ?? 0 = $9 and ?? 0 = $15. d. [2 marks] Determine all bundles for which the marginal utility per dollar spent on each of the two goods is equalized. e. [3 marks] What is Cassandra’s optimal consumption bundle? Represent this bundle on your graph obtained in part (a) and denote it by ?0. Draw Cassandra’s indifference curve at the optimal consumption bundle and denote it by ?0. f. [7 marks] Now assume that the price of frozen Dinners decreases and is now ?? 1 = $5. Assume that the price of Take-out meals and Cassandra’s income have not changed. Re- do parts (a) to (e) for prices. ?? 1 = $5 and ?? 0 = $15. Plot the new budget line, the new Page 3 of 4 optimal consumption bundle, ?1, and the new indifference curve, ?1, on the same graph obtained in part (a). g. [3 marks] Indicate the substitution effect (SE) and income effect (IE) of a decrease in the price of Dinners from ?? 0 = $9 to ?? 1 = $5 on your graph, assuming that frozen Dinners are an inferior good. h. [4 marks] Assuming that frozen Dinners are an inferior good, how much money income would Cassandra’s parents (Hecuba and Priam) have to take away from her so that, at the new prices, ?? 1 = $5 and ?? 0 = $15, bundle ???? consisting of 12 Dinners and 4 Take-out meals gives Cassandra the same utility as bundle ?0? 3. [20 marks] A terrorist group has indifference curves (which obey the four properties of indifference curves for ordinary goods) over terrorist activities (T) and non-terrorist activities (N). The terrorist group faces a resource constraint ?? ∙ ? + ?? ∙ ? = ?, where ?? and ?? are the unit costs of generic terrorist (T) and non-terrorist actions (N), and I is the groups income or resources for the current period. a. [2 marks] If the terrorists devote all of their resources to terrorist attacks, how many attacks can they accomplish? b. [2 marks] If the terrorists devote all of their resources to non-terrorist activities, how many non-terrorist activities can they accomplish? c. [3 marks] Draw the terrorist group’s resource constraint with terrorist activities (T) on the horizontal axis. [The intercepts are arbitrary since you do not have numbers for the costs of the two activities and the group’s resources.] d. [3 marks] The terrorist group is choosing the optimal bundle of terrorist (T) and non- terrorist (N) activities to maximize utility subject to the resource constraint. Indicate the optimal bundle and the corresponding indifference curve on your previous diagram. [Pick an arbitrary bundle as, again, you do not have numbers for the costs of the two activities and the group’s resources.] e. [5 marks] The government is engaging in proactive measures to reduce the terrorist group’s resources, I. Illustrate this situation on your previous diagram, indicating the new optimal combination of terrorist and non-terrorist activities. Be explicit about the assumptions you make regarding the two types of activities (i.e. normal or inferior goods). [Either assumption is fine as long as you justify it and draw a diagram that is consistent with your assumption.] f. [5 marks] Now consider an alternative defensive policy which increases the cost of terrorist activities for the group. Illustrate this situation on a separate diagram, indicating the new optimal combination of terrorist and non-terrorist activities chosen by the terrorist group. Indicate the substitution and income effects on your diagram. Page 4 of 4 4. [30 marks] Milo Minderbinder runs M&M Enterprises which produces crates of tangerines. Milo hires soldiers in Italy at $10 per day and rents one plane at $50 per day. Milo buys crates of tangerines in Morocco and pays local workers $1 per crate. M&M Enterprises’ total product schedule is given by the following table: L (soldiers) Q (crates of tangerines) 1 10 2 30 3 45 4 52 5 57 6 59 7 60 where labour, L, is measured in numbers of soldiers hired and output, Q, in numbers of crates of tangerines. a. [4 marks] Plot M&M’s total product curve (Graph 1). b. [7 marks] Determine the marginal product of labour (???) of each unit of labour; determine the average product of labour (??) at each level of labour; plot the marginal product and the average product curves on the same graph (Graph 2). What is the shape of the marginal product of labour curve? How do you interpret this? c. [6 marks] Determine M&M’s total fixed cost (???), total variable cost (???), and total cost (??) of production at each level of output. Plot the total fixed cost, variable cost, and total cost curves on the same graph (Graph 3). d. [8 marks] Determine M&M’s average fixed cost (???), average variable cost (???), and average total cost (???) at each level of output. Plot the average fixed cost, average variable cost, and average total cost on the same graph (Graph 4). What is the shape of the average fixed cost? What about that of the average variable cost and average total cost? What explains the shape of these curves? e. [5 marks] Determine M&M’s marginal cost (??) at each level of output. Plot the marginal cost curve on Graph 4 obtained in part (d). What is the relationship between the average total cost and the marginal cost curves?