Final answer:
The Aggregate Demand curve is derived by combining the IS and LM equations, eliminating the interest rate to express output in terms of the price level, showing a downward-sloping relationship between price level and output.
Step-by-step explanation:
To derive the Aggregate Demand (AD) curve using the IS and LM equations, we combine the two to eliminate the interest rate variable and express output (Y) in terms of the price level (P). The given IS equation is: Y = 1900 - 100r, where Y is output and r is the interest rate. The LM equation is M/P = 100 = -1000 + 100r, which in our case, rearranges to r = M/(100P) + 10. To combine the two, we substitute the expression for r from the LM into the IS, resulting in Y = 1900 - 100(M/(100P) + 10). Simplifying this, Y = 1900 - M/P - 1000. Assuming that M is fixed, we notice that a decrease in P leads to an increase in Y, indicating that the AD curve slopes downward. The final AD equation characterizes the relationship between the price level and output, capturing the idea that as the price level falls, aggregate demand for goods and services increases.