DEMOLEC5
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Demonstration Lecture 5: Suggested Solutions 1. True. The analysis underpinning the economy-wide short run aggregate supply curve is based on the derivation of the relevant supply curve for an individual firm. The first point to note is that an individual firm will produce up to the point where price of the product or service equals its relevant marginal cost. This is the firm’s profit-maximising condition. It also follows that in a perfectly competitive market that price will equal marginal revenue. Having established those criteria, the next step is to consider the individual firm’s production function in the short- run. Assuming that the production function comprises a variable labour input, a fixed capital stock input, and a fixed level of technology, the marginal physical product of labour is the extra output that a firm can produce by adding an extra unit of labour input. The latter is presumed to show diminishing returns, or have a diminishing marginal physical product of labour for a given factor price (or money wage rate say per hour of labour). Students should refer to pages 13-15, Chapter 4, in the Brooks manuscript to see the relevant diagrams illustrating these relationships. The law of diminishing returns implies that the individual firm’s marginal cost (of production) curve will be upwards sloping. In effect the latter curve is the individual firm’s supply curve, and so upwards sloping indicating that higher prices will induce higher levels of output in the short-run. 2. True. The answer to this question builds on the previous answer. The key point to note is that one can establish a relationship between the marginal physical product of labour (MPPL), the individual firm’s marginal cost of production (MC), and the money wage rate (W). Assuming a constant or fixed money wage rate in the first instance, MC = W/ MPPL. Next , note that the profit-maximising criterion for an individual firm is to produce up to that level of production where MC = Price. Therefore P (or price) = MC = W/ MPPL. If P = W/ MPPL, it follows that by re-arranging the equation that MPPL = W/P. Logically one can say that the MPPL is equivalent to a firm’s demand for labour schedule. Furthermore a firm will be more likely to hire more labour when W/P (or the real wage) is lower rather than higher. The demand for labour curve is therefore downwards sloping, as shown in the first of three diagrams on page 16 of Chapter 4 of the Brooks manuscript. By determining varying levels of labour demand at different levels of real wages (W/P), it then possible to see what levels of output, Y, are achievable given the specification of the original production function., as shown in the second diagram on page 16. Finally by plotting the various price levels from the labour demand curve against the output levels from the production function, the third and final SRAS curve is obtained. Note that the latter is constructed for a
Transcript of DEMOLEC5
Demonstration Lecture 5: Suggested Solutions
1. True. The analysis underpinning the economy-wide short run aggregate supply curve is based on the derivation of the relevant supply curve for an individual firm. The first point to note is that an individual firm will produce up to the point where price of the product or service equals its relevant marginal cost. This is the firm’s profit-maximising condition. It also follows that in a perfectly competitive market that price will equal marginal revenue. Having established those criteria, the next step is to consider the individual firm’s production function in the short-run. Assuming that the production function comprises a variable labour input, a fixed capital stock input, and a fixed level of technology, the marginal physical product of labour is the extra output that a firm can produce by adding an extra unit of labour input. The latter is presumed to show diminishing returns, or have a diminishing marginal physical product of labour for a given factor price (or money wage rate say per hour of labour). Students should refer to pages 13-15, Chapter 4, in the Brooks manuscript to see the relevant diagrams illustrating these relationships. The law of diminishing returns implies that the individual firm’s marginal cost (of production) curve will be upwards sloping. In effect the latter curve is the individual firm’s supply curve, and so upwards sloping indicating that higher prices will induce higher levels of output in the short-run.
2. True. The answer to this question builds on the previous answer. The key point to note is that one can establish a relationship between the marginal physical product of labour (MPPL), the individual firm’s marginal cost of production (MC), and the money wage rate (W). Assuming a constant or fixed money wage rate in the first instance, MC = W/ MPPL. Next , note that the profit-maximising criterion for an individual firm is to produce up to that level of production where MC = Price. Therefore P (or price) = MC = W/ MPPL. If P = W/ MPPL, it follows that by re-arranging the equation that MPPL = W/P. Logically one can say that the MPPL is equivalent to a firm’s demand for labour schedule. Furthermore a firm will be more likely to hire more labour when W/P (or the real wage) is lower rather than higher. The demand for labour curve is therefore downwards sloping, as shown in the first of three diagrams on page 16 of Chapter 4 of the Brooks manuscript. By determining varying levels of labour demand at different levels of real wages (W/P), it then possible to see what levels of output, Y, are achievable given the specification of the original production function., as shown in the second diagram on page 16. Finally by plotting the various price levels from the labour demand curve against the output levels from the production function, the third and final SRAS curve is obtained. Note that the latter is constructed for a given money wage; a given level of capital stock; and a given technology level. These are all shift parameters of the SRAS.
3. True. In a competitive world the AD and SRAS curves intersect so as to determine the price level. In turn the money wage rate, W, responds to that price level to determine a market-clearing real wage rate, W/P. As flexible wages and prices, in time, provide a full-employment outcome, then it follows that the price outcome determined in the product market must be consistent with AD and the SRAS being equal at the full-employment level. Competition should lead to simultaneous balance in both the labour and product markets. In turn this implies the existence of a vertical LRAS at the full-employment level of output. For a useful illustration of this relationship students should examine the 2 diagrams in Section 4.2.3 of the Brooks manuscript.
4. True. The LRAS is vertical at the full-employment level of output. Students should refer to the pair of diagrams located in Section 4.2.4 of the Brooks manuscript, page 21. Commencing at the short-run equilibrium point A (with an equilibrium real wage of Wo/Po), a fiscal expansion will lead to a rightward shift of the AD curve from AD0 to AD1. Therefore the price level increases form Po to P1, and so movement to point C results. The higher price level of P1 will lead to disequilibrium in the labour market, as it now produces a real wage result of Wo/P1, which is the same as a reduction in the real wage rate. The latter produces a situation whereby demand for labour will exceed the supply of labour at that specific real wage rate. Eventually money wage rates will have to increase, and so W1 results. This however will move the SRAS from its original position to SRAS(W1), and so a reduced level of Y results, together with a higher price level. Again labour market disequilibrium will result, and eventually a higher money wage rate will be needed to clear the labour market. This process will continue until point Z is reached and that is consistent with a price level of Px and the full-employment level of Yo. Simultaneous
labour and product market equilibrium are achieved. Once again it demonstrates that the LRAS is vertical at the full-employment level of output.
5. True. The key point to note in answering this question is to be able to understand the difference between the effect upon the SRAS of a change in the price level, and the effect upon the SRAS and the LRAS of a change in the overall supply of labour. The initial change in price, assuming a given money wage rate, will cause disequilibrium in the labour market, which will only be resolved by an eventual increase in the money wage rate. This will shift the SRAS back to the left. On the other hand an increase in the supply of labour will move the labour supply curve to the right, within the labour market. This would in turn lead to a change in the money wage rate causing a shift of the SRAS. However, because the total labour supply has changed, a new full-employment level would result. Logically this would lead to the LRAS shifting as well.
6. True. Students should refer to the appropriate definitions in Gordon, 7 th edition, page 210. (or if you are using the 6th edition, refer to page 163)
