I just need help with questions 2,3 and 4. I have already solved question 1.Econ 201: Assignment #1...

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I just need help with questions 2,3 and 4. I have already solved question 1.Econ 201: Assignment #1 Fall 2022 Josh Boitnott Instructions: • Show your work if you want partial marks. Wrong answers with no work shown will receive a mark of 0. • I encourage you to work with others; however, you must submit your own version of the assignment. Further to that, I request that you not publicly post solutions for others to copy. • The answers need to be submitted through Crowdmark and are due by Oct. 14th at 11:59 pm. You will need to submit/upload your solutions through Crowdmark with the link initial link to the submission sent via e-mail by Crowdmark. • Please make sure to submit your answers in the correct position; we should be able to read your answers without having to rotate them. Finally, when capturing the image of your work, please make sure to have sufficient lighting and clarity of the images. 1. (14 marks) Suppose the market for laser pointers consists of 2 types of people: profes- sors and cat lovers. The professors have an individual demand of qProf = 13− 1 5 P and the cat lovers have an individual demand of qCat = 20− 1 2 P . (a) (4 marks) If there are 30 consumers with a demand of qProf and 8 consumers with a demand of qCat, then what is the (inverse) market demand curve P (Q D) (for all 38 people)? Illustrate it in a graph. (b) (4 marks) Suppose the (inverse) market supply curve is P = 1 15 QS, what is the market equilibrium outcome? (Hint: Both groups buy laser pointers and your quantity should be somewhere between 250 and 400.) What is the consumer and producer surplus in this case? (Reminder: Your consumer surplus will be ugly to calculate since the demand curve is discontinuous). (c) (6 marks) The government has become concerned about long term environmental harm from improper disposal of the laser pointers. To alleviate some of the burden, the government decides to impose a $7.50 excise tax on each laser pointer sold. What is the new equilibrium? How much has the government raised in tax revenue? How big is the dead weight loss? What is the tax incidence for the consumers? 2. (18 marks) Suppose you are told that a consumer has the following utility function: U(qx, qy) = e (qy) × √ 2qx − 1. Their income is Y , the price of good x is Px, and the price of good y is Py. (a) (3 marks) Show that the Marginal Rate of Substitution is the same for U(qx, qy) as the positive monotonic transformation W = ln(U(qx, qy)). What type of utility function is W (qx, qy)? (b) (4 marks) Find q∗x, the demand for good x, and q ∗ y , the demand for good y. Hint : be sure to include information about where the function works. (c) (7 marks) Suppose you are given Px = $2 and Py = $18, provide a sketch of of the income-consumption curve for Y = {20, 25, 30, 35, 40, 45}. Be sure to label the points for each income and clearly indicate what is happening (i.e. values of qx and qy corresponding to each Y ). (d) (4 marks) Find the cross price elasticity of demand for q∗x and q ∗ y. Does this tell you anything about the relationship between the two goods? 3. (17 marks) This question is designed to examine how we can utilize our basic theory without having an explicit indifference curve. Suppose Lia has an income of Y = $500 and only consumes two good: memory sticks (to store free economics papers she downloads from the library) and hardcover novels (which she refuses to check out from the library). Furthermore, let the price of memory sticks be PS = $25 and the price of hardcover novels be PN = $20. (a) (5 marks) Create a graph of Lia’s behaviour with the assumption that her utility is consistent with our normal assumptions (e.g. ∂U/∂qi > 0 and ∂ 2U/∂q2i

Rhea · Accepted Answer

2.
(a)
is a quasi-linear utility function of the form  where  is a constant.
(b)
A demand function relates the quantity demanded of a good by a consumer with the price of the good, i.e. we need to find 
Setting up the optimization problem:
subject to: 
where 
Using these values the optimization problem becomes:
subject to: 
Setting this up as a Lagrange problem,
Taking the first order conditions, we get:
We would usually take the second order conditions to ensure that we have a maximum. But clearly we have a maximum in this case since  is strictly increasing in  and .
Combining  and  we get-
And substituting the value of  in  constraint we get-
(c)
Given,  and .
We need to draw an Income consumption graph for 
	Y
	Budget Line
	Name
	Max x for income Y
	Max y for income Y
	Equilibrium point for Income Y
	20
	2x+18y=20
	L1
	X1
	Y1
	E1
	25
	2x+18y=25
	L2
	X2
	Y2
	E2
	30
	2x+18y=30
	L3
	X3
	Y3
	E3
	35
	2x+18y=35
	L4
	X4
	Y4
	E4
	40
	2x+18y=40
	L5
	X5
	Y5
	E5
	45
	2x+18y=45
	L6
	X6
	Y6
	E6
For ease in typing  and are substituted with x and y respectively.
As the income increases, the purchasing power of the consumer increases. This is well illustrated by the budget lines L1, L2, L3, L4, L5, and L6. If we take Income i.e. Y=20$, then we plot the corresponding budget line. 
Corresponding to this line, when , then . This point is X1 where the line cuts the X axis. Similarly, we have Y1. 
We know that indifference curves are curves along which there is no change in utility obtained from the purchase and the budget lines makes a tangent. In other words, along indifference curves, utility is constant. So, we draw indifference curves by drawing 
 such that it touches the budget line at only one point. We see that as our income increases, we opt for higher indifference curves. The point where the indifference curve touches the budget line corresponding a particular income is the equilibrium point. Here, we have 6 equilibrium points namely E1, E2, E3, E4, E5, and E6.

Econ 201: Assignment #1Fall 2022Josh BoitnottInstructions:• Show your work if you want partial marks. Wrong answers with no work shownwill receive a mark of 0.• I encourage you to work...

Answer To: Econ 201: Assignment #1Fall 2022Josh BoitnottInstructions:• Show your work if you want...

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