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Question 1: [50 Points] The Doctor only consumes both Sonic Screwdrivers (s) and Tardis (t). He has a strong preference for having exactly as many Sonic Screwdrivers as Tardis at his disposal. In fact, his preference can be represented by the utility function: U(s,t) = min{2t - s, s}. [Hint: The Doctor does not have a perfect complement preference, or an "L"-shape indifference curve with a 90-degree angle as discussed in class.] a. [6 Points] The Doctor currently has 1 Sonic Screwdriver and 1 Tardis. What utility does he have? If he acquires a second Sonic Screwdriver (s = 2 and t = 1), would that make him better or worse or the same? What if he acquires a second Tardis (s = 1 and t = 2)? Please explain. b. [4 Points] If for some amounts of t and s, such that min{2t - s, s} = s, are there more, fewer, or an equal number of Sonic Screwdrivers compared to Tardis? Why? c. [4 Points] If for some amounts of t and s, such that min{2t - s, s} = t, are there more, fewer, or an equal number of Sonic Screwdrivers compared to Tardis? Why? Draw a graph with s on the x-axis and t on the y-axis. Then draw the following lines on the same graph and answer the corresponding questions. d. [5 Points] Draw the line at which s = t. Show coordinates of at least two points on the line. What point on the line would give the Doctor a utility of 10 (How many Screwdrivers, and how many Tardis?)? e. [3 Points] Draw the line s = 10. Show coordinates of at least two points on the line. f. [3 Points] Draw the line 2t - s = 10. Show coordinates of at least two points on the line. g. [10 Points] Highlight the segment of the line s = 10 and the segment of the line 2t - s = 10 that belong to the Indifference curve, on which all the points have the same utility level U = 10.

          Question 1: [50 Points] The Doctor only consumes both Sonic Screwdrivers (s) and Tardis (t). He has a strong preference for having exactly as many Sonic Screwdrivers as Tardis at his disposal. In fact, his preference can be represented by the utility function:

U(s,t) = min{2t - s, s}.

[Hint: The Doctor does *not* have a perfect complement preference, or an "L"-shape indifference curve with a 90-degree angle as discussed in class.]

a. [6 Points] The Doctor currently has 1 Sonic Screwdriver and 1 Tardis. What utility does he have? If he acquires a second Sonic Screwdriver (s = 2 and t = 1), would that make him better or worse or the same? What if he acquires a second Tardis (s = 1 and t = 2)? Please explain.

b. [4 Points] If for some amounts of t and s, such that min{2t - s, s} = s, are there more, fewer, or an equal number of Sonic Screwdrivers compared to Tardis? Why?

c. [4 Points] If for some amounts of t and s, such that min{2t - s, s} = t, are there more, fewer, or an equal number of Sonic Screwdrivers compared to Tardis? Why?

Draw a graph with s on the x-axis and t on the y-axis. Then draw the following lines on the same graph and answer the corresponding questions.

d. [5 Points] Draw the line at which s = t. Show coordinates of *at least* two points on the line. What point on the line would give the Doctor a utility of 10 (How many Screwdrivers, and how many Tardis?)?

e. [3 Points] Draw the line s = 10. Show coordinates of *at least* two points on the line.

f. [3 Points] Draw the line 2t - s = 10. Show coordinates of *at least* two points on the line.

g. [10 Points] Highlight the segment of the line s = 10 and the segment of the line 2t - s = 10 that belong to the Indifference curve, on which all the points have the same utility level U = 10.

question 1 50 points the doctor only consumers both sonic screwdrivers s and tardis t he has a strong preference for having exactly as many sonic screwdrivers as tardis at his disposal in fa 65523

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