The Demand for Lamp UK consumption of lamb: 1974-2004 140 130 120 110 100 90 Grams per person per week 80 70 60 50 40 30 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 The diagram shows what happened to the consumption of lamb in the UK over the period 1974-2004. How can we explain this dramatic fall in consumption? One way of exploring this issue is to make use of a regression model, which should help us to see which variables are relevant and how they are likely to affect demand. The following is an initial model fitted (using the Microfit statistical software package) to annual data for the years 1974-2004. QL = 170.2 - 0.197PL - 0.069PB + 0.280Pp - 0.0094Y (1) where Qu is the quantity of lamb sold in grams per person per week; PL is the 'real' price of lamb (in pence per kg, 1985 prices); PB is the 'real' price of beef (in pence per kg, 1985 prices); Pp is the 'real' price of pork (in pence per kg, 1985 prices); Y is households' real disposable income per head (E per year, 2002 prices). Question 1: (25 points) This model makes it possible to predict what would happen to the demand for lamb if any one of the four explanatory variables changed, assuming that the other variables remained constant. Using equation (1), calculate what would happen - ceteris paribus - to the demand for lamb if: a. the real price of lamb went up by 10p per kg; b. the real price of beef went up by 10p per kg; C. the real price of pork fell by 10p per kg; d. real disposable income per head rose by $100 per annum. Are the results as you would expect?There a serious problem with estimated demand functions like these: they assume that other determinants of demand (i.e. those not included in the model) have not changed. In the case of this demand-for-lamb function. one of the other determinants did change. This was tastes during the 1980s and 1990s there was a shift in demand away from lamb and other meats, partly for health reasons. and partly because of an expansion in theavailability of and demand for vegetarian and low-meat altematives. On the assumption that this shift in taste took place steadily over time, a new demand equation was estimated for the same years: CL = 143.7 - 0.278PL - 0.03DPB + 0.116PP + 0.0062Y - 3.787TIME (2) where TIME =1 in 1974, 2 in 1975, 3 in 1976, etc. Question 2: (20 points) How does the introduction of the variable TIME affect the relationship between the demand for lamb and (a) its real price; (b) real disposable income per head? Question 3: (25 points) Does lamb now appear to be a normal good or an inferior good? Explain why (30 points} Question 4: (30 points) What does the negative coefficient of Pa indicate? ls model (2) a perfect model? Explain why. (35 points)