Based on the following stock price and shares outstanding information, compute the beginning and ending values for a price$-$weighted index and a market$-$value$-$weighted index.

$\backslash$table$[[,$DECEMBER $31,2002,$DECEMBER $31,2003,],[,$Price,Shares Outstanding,,Price,Shares Outstanding$],[$Stock $K,20,100,000,000,32,100,000,000,],[$Stock $L,80,2,000,000,45,4,000,{000}^a,],[$Stock $M,40,25,000,000,42,25,000,000,]]$

a$.$ Compute the percentage change in the value of each index.

b$.$ Explain the difference in results between the two indexes.

c$.$ Compute the results for an unweighted index and discuss why these results differ from the others.