# Homework Assignment Algebra

Instructor: Ram Sewak Dubey ECON 317: Problem Set 2 September 28, 2018

1. [Graph I – Demand Function]

A complete demand fucntion is given by the equation

Qd =−30P+0.05Y +2Pr +4T

wherer P is the price of the good, Y is the income, Pr is the price of a related good (here it is a substitute, why?) and T is the taste parameter.

(a) Can we graph this function?

(b) Draw the graph of the demand function, by assuming Y = 6000, Pr = 20, and T = 30.

(c) Describe in words, as to what does a typical demand function, like the one here, shows?

(d) What happens to the graph if the price of the good changes from $5 to $8?

(e) What happens to the graph when T changes from 30 to 40; or income increases from 6000 to 8000.

(f) In economics, we typically draw the demand curve by graphing the independent vari- able (price, P) on the vertical axis and the dependent variable (quantity Qd) on the horizontal axis. For this we modify the demand function to inverse demand function. What is the inverse demand function for the above demand.

2. [Graph II – Budget Line]

A person has $120 to spend on two goods (x and y) whose respective prices are $3 and $5 per unit.

(a) Draw the budget line showing all the different combinations of the two goods that can be bought with the given budget.

(b) What happens to the budget line if the budget (money available to spend) falls by 25%.

(c) What happens to the budget line if the price of good x doubles?

(d) What happens to the budget line if the price of good y falls to $4?

(e) Bonus Question Consider a scheme of quantity discount where is you buy more than 20 units of good x for each additional unit the price of good x is lower by 50%. Draw the new budget line.

Submission deadline: October 3, 2018 11:59 pm Page 1 of 4

Instructor: Ram Sewak Dubey ECON 317: Problem Set 2 September 28, 2018

3. [Graph III – Isocost Curve]

Either coal (x) or gas (y) can be used in the production of steel. The cost (per unit) of coal is 100, the cost (per unit) of gas is 500. Draw an isocost curve showing the different combinations of gas and coal that can be purchased

(a) with an initial expenditure (TC) of 20000.

(b) if the expenditure (TC) increases by 50%.

(c) if the gas price is reduced by 25%.

(d) if the coal price rises by 20%.

In answering parts (b)-(d), always start from the original isocost equation.

4. [Graph IV – National Income Model]

Let AE =C+ I +G+NX

where AE is the aggregate expenditure, C is the consumption function, I is investment, G is government expenditure and NX is the net export. Given

C = 50+0.8Y

where Y is the national income and I0 = 50

(a) Graph the consumption function.

(b) Graph the aggregate expenditure function by taking the values G0 = 0 and NX = 0.

(c) Find the equilibrium level of income from the graph.

(d) Find the equilibrium level of income without using graph analytically.

(e) Next, change the value of government expenditure to G0 = 50 and find the equilibrium level of income.

(f) The consumption function should ideally depend on the disposable income Yd which is the total income Y minus the taxes T . With this, consumption function changes to C = 50+ 0.8Yd . Compute the equilibrium level of income when I0 = 50 and G = NX = 0.

(g) Compute the equilibrium level of income in the previous part when I0 = 50 and G= 50 and NX = 0.

Submission deadline: October 3, 2018 11:59 pm Page 2 of 4

Instructor: Ram Sewak Dubey ECON 317: Problem Set 2 September 28, 2018

5. [Graph V – Production Possibility Frontier (PPF) or Production Possibility Curve (PPC)]

Note: It is helpful to review the ECON 102 textbook and notes on the comparative advan- tage and production possibility frontier for this question. Adam, Ben and Chris are in the auto-repair business and and each has his own workshop. They offer brake repair and clutch repair services. Adam can do following combinations of the number of brake repairs and clutch repairs in a day.

Brakes Clutches 30 30 0 60

(a) Find the equation for the production possibility frontier (PPF) for Adam given the information above. Use notation “B” for number of brake repair and “C” for number of clutch repair jobs. Assume that the PPF is a straight line. Draw a graph to show the PPF with number of brake repairs on the vertical axis and number of clutch repairs on the horizontal axis. Hint: To find the equation of straight line, we need only a pair of observation points.

(b) How many brake repair jobs can Adam do if he does only brake repairs in a day?

Ben can do following combinations of the number of brake repairs and clutch repairs in a day.

Brakes Clutches 24 36 48 0

(A) Find the equation for the production possibility frontier (PPF) for Ben given the in- formation above. Assume that the PPF is a straight line. Draw a graph to show the PPF with number of brake repairs on the vertical axis and number of clutch repairs on the horizontal axis.

(B) How many clutch repair jobs can Ben do if he does only clutch repairs in a day?

Chris can do following combinations of the number of brake repairs and clutch repairs in a day.

Brakes Clutches 16 16 8 32

Submission deadline: October 3, 2018 11:59 pm Page 3 of 4

Instructor: Ram Sewak Dubey ECON 317: Problem Set 2 September 28, 2018

(I) Find the equation for the production possibility frontier (PPF) for Chris given the information above. Assume that the PPF is a straight line. Draw a graph to show the PPF with number of brake repairs on the vertical axis and number of clutch repairs on the horizontal axis.

(II) How many clutch repair jobs can Chris do if he does only clutch repairs in a day?

(III) How many brake repair jobs can Chris do if he does only brake repairs in a day?

Adam and Ben are planning to work together.

(i) Draw a graph to show the PPF with number of brake repairs on the vertical axis and number of clutch repairs on the horizontal axis, when they work together.

(ii) How many clutch repair and brake repair jobs, they can do if each specializes in the job of their comparative advantages?

(iii) How many brake repair jobs they can do if they do only brake repairs, in a day?

(iv) How many clutch repair jobs they can do if they do only clutch repairs, in a day?

Now that we see the two working together can do more jobs, we next want to examine it it makes sense for them to invite Chris to join.

(1) Draw a graph to show the PPF with number of brake repairs on the vertical axis and number of clutch repairs on the horizontal axis, when all three work together.

(2) How many clutch repair and brake repair jobs, they can do at the point(s) on the PPF where there is a change in slope.

(3) How many brake repair jobs they can do if they do only brake repairs, in a day?

(4) How many clutch repair jobs they can do if they do only clutch repairs, in a day?

Submission deadline: October 3, 2018 11:59 pm Page 4 of 4

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