QUESTION 6 (a) The bar shown in Figure Q2(a) is subjected to tensile load of 150 Kn. If the stress in the middle portions is limited to 160 N/mm², determine the diameter of the middle portion. Find also the length of the middle portion if the total elongation of the bar is to be 0.25 mm. E E = 2.0 + 105N/mm². (12 marks) 150 KN 10 cm DIA 10 cm DIA 150 KN 45 cm Figure Q6(a) (b) A brass bar, having cross-section area of 900 mm², is subjected to axial forces as shown in Figure Q2(b), in which AB = 0.6 m, BC = 0.8 m, and CD = 1.0 m. Find the total elongation of the bar. E = 1.0 + 105N/mm2 . (8 marks) Page 4 of 5 B D 40 KN 70 KN 20 KN 10 KN Figure Q6(b) (TOTAL = 20 MARKS)

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Question:

IS-LM Model Freeland, a country in a faraway galaxy, anticipates being hit by rough weather in the coming few years. This is expected to decrease the future productivity of capital, and as a result, businesses in Freeland have less desire to invest. This question will help you analyze the effect of this anticipated shock on future productivity. The Freeland economy is described by the following set of equations.

Goods Market Goods Market Equilibrium Condition: 𝑌=𝐶+𝐼+𝐺

Consumer Demand: 𝐶=0.5(𝑌−𝑇) I

nvestment Demand: 𝐼=60𝑍−50𝑟

Government Budget: 𝐺=𝑇=400

Money Market Money Market Equilibrium: 𝑀𝑃=𝐿(𝑌,𝑟+𝜋𝑒)

Real Money Demand: 𝐿(𝑌,𝑟+𝜋𝑒)=0.5𝑌−50𝑟

Money Supply: 𝑀=480

Labor Market Full-Employment Output: 𝑌¯=500

The variable Z captures the anticipated shock to future productivity. If they become pessimistic, Z goes down. If they become optimistic, Z goes up.

1.) Derive the IS curve for any given Z.

2.) Derive the LM curve.

3.) Suppose that the economy has been at the long-run equilibrium with 𝑍=1.5. Find the corresponding long-run equilibrium values of output, interest rate, and the price level.

4.) Suppose that due to the anticipated future shock, Z decreases to 𝑍=1. Compute the short-run equilibrium values of output, real interest rate, and the price level.

5.) Suppose that Z remains at 𝑍=1. What are the new long-run equilibrium values of output, real interest rate, and the price level?

6.) Using the IS-LM-FE model, show the effect of the anticipated future shock graphically. On your graph, show the initial long-run equilibrium, the short-run equilibrium, and the new long-run equilibrium.

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Answer:

Solution 

Answer1: Derive the IS Curve.  

The IS curve represents all combinations of income (Y) and the real interest rate (r) such that the market for goods and services is in equilibrium. That is, every point on the IS curve is an income/real interest rate pair (Y,r) such that the demand for goods is equal to the supply of goods (where it is implicitly assumed that whatever is demanded is supplied) or, equivalently, desired national saving is equal to desired investment.

Consider an initial equilibrium in the goods market where r = 5% and income is equal to Y0. This equilibrium is illustrated in the graph on the right with r on the vertical axis and Y on the horizontal axis as the big black dot (middle dot). Now suppose Y increases to Y1 (say supply increases). This increase in Y shifts the desired savings curve down and right lowering the equilibrium real interest rate to 3%. The new equilibrium in the goods market with higher income and a lower real interest rate is illustrated in the graph on the right as the big blue dot (bottom dot). Similarly, if Y decreases from Y0 to Y2 then the savings curve shifts up and left and the equilibrium real interest rises. The new equilibrium in the goods market with lower income and a higher real interest rate is illustrated in the graph on the right as the big red dot (top dot). Notice that as income increases (decreases) the real interest must fall (rise) in order to maintain equilibrium in the goods market. This is the relationship that is represented in the downward sloping IS curve.   

Derivation of IS curve.

 

 

Answer 2: Derivation  LM curve, "L"

denotes Liquidity and "M" denotes money, is a graph of combinations of real income, Y, and the real interest rate, r, such that the money market is in equilibrium (i.e. real money supply = real money demand). The graphical derivation of the LM curve is illustrated below.

 

 

 

The left-hand side of the graph illustrates money market equilibrium for a given level of Y. For example, when Y = Y0 the equilibrium real interest rate is 5%. The right-hand-side of the graph gives the LM curve. The LM curve is plotted with the real interest rate on the vertical axis and real income (GDP) on the horizontal axis. Each point on the LM curve represents a money market equilibrium for a particular real interest rate and income pair (r, Y). For example, the money market equilibrium at (r=5%, Y=Y0) is given by the black (middle) dot on the LM curve.

 

At a higher level of income, Y1 > Y0, the money demand curve shifts up and right and a new equilibrium occurs at r = 7%. This equilibrium is represented by the blue (upper) dot on the LM curve. Similarly, at a lower level of income Y2 < Y0 the money demand curve shifts down and left and a new equilibrium occurs at r = 3%. This equilibrium is given the by the red (lower) dot on the LM curve.

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