Return to the demand-and-supply model given in Eqs. (20.3.1) and (20.3.2).

Suppose the supply function is altered as follows:

Q_t = β₀ + β₁P_tˆ’1 + u_2t

where P_tˆ’1 is the price prevailing in the previous period.

a. If X (expenditure) and Ptˆ’1 are predetermined, is there a simultaneity problem?

b. If there is, are the demand and supply functions each identified? If they are, obtain their reduced-form equations and estimate them from the data given in the following table.

c. From the reduced-form coefficients, can you derive the structural coefficients? Show the necessary computations.

Real per Capita Personal Consumption Expenditure, X Index of Crop Production Index of Crop Prices Received by Farmers (19901992 = 100), P Observation (1996 = 100), Q 4,789 5,282 5,804 6,417 7,073 7,716 8,439 8,945 9,775 10,589 11,406 12,048 12,766 13,685 14,546 15,349 15,722 16,485 17,204 18,004 18,665 19,490 20,323 21,291 22,491 23,862 24,722 25,501 26,463 27,937 1975 66 88 1976 67 87 83 89 98 1977 71 1978 73 1979 78 1980 75 107 1981 81 111 82 1982 98 1983 71 108 1984 81 111 85 98 1985 1986 82 87 1987 84 86 1988 1989 80 86 90 104 109 103 1990 1991 90 101 1992 96 101 1993 91 102 105 1994 101 112 1995 96 1996 100 127 1997 104 115 1998 105 107 1999 108 97 2000 108 96 2001 108 99 2002 107 105 2003 108 111 2004 112 117